Updated on 2022/05/25

写真a

 
KAWASHIMA, Shuichi
 
Affiliation
Faculty of Science and Engineering, Global Center for Science and Engineering
Job title
Professor(without tenure)

Concurrent Post

  • Faculty of Political Science and Economics   School of Political Science and Economics

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Education

  • 1978.04
    -
     

    京都大学大学院   工学研究科   数理工学専攻 博士課程  

  • 1978.04
    -
     

    京都大学大学院   工学研究科   数理工学専攻 博士課程  

  • 1976.04
    -
    1978.03

    京都大学大学院   工学研究科   数理工学専攻 修士課程  

  • 1976.04
    -
    1978.03

    京都大学大学院   工学研究科   数理工学専攻 修士課程  

  • 1972.04
    -
    1976.03

    Kyoto University   Faculty of Engineering  

Degree

  • 京都大学   工学博士

Research Experience

  • 2018.04
    -
     

    Waseda University   Faculty of Science and Engineering

  • 1994.06
    -
     

    九州大学   数理学研究院   教授

  • 1994.06
    -
     

    Kyushu University

  • 1986.10
    -
     

    Kyushu University   School of Engineering

  • 1985.01
    -
     

    Nara Women's University   Faculty of Science

  • 1981.04
    -
     

    Nara Women's University   Faculty of Science

▼display all

Professional Memberships

  •  
     
     

    日本学術振興会

  •  
     
     

    日本数学会

 

Papers

  • New structural conditions on decay property with regularity-loss for symmetric hyperbolic systems with non-symmetric relaxation

    Yoshihiro Ueda, Renjun Duan, Shuichi Kawashima

    Journal of Hyperbolic Differential Equations   15 ( 1 ) 149 - 174  2018.03

     View Summary

    This paper is concerned with the weak dissipative structure for linear symmetric hyperbolic systems with relaxation. The authors of this paper had already analyzed the new dissipative structure called the regularity-loss type in [Y. Ueda, R. Duan and S. Kawashima, Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application, Arch. Ration. Mech. Anal. 205 (2012) 239-266]. Compared with the dissipative structure of the standard type in [T. Umeda, S. Kawashima and Y. Shizuta, On the devay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435-457
    Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275], the regularity-loss type possesses a weaker structure in the high-frequency region in the Fourier space. Furthermore, there are some physical models which have more complicated structure, which we discussed in [Y. Ueda, R. Duan and S. Kawashima, Decay structure of two hyperbolic relaxation models with regularity loss, Kyoto J. Math. 57(2) (2017) 235-292]. Under this situation, we introduce new concepts and extend our previous results developed in [Y. Ueda, R. Duan and S. Kawashima, Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application, Arch. Ration. Mech. Anal. 205 (2012) 239-266] to cover those complicated models.

    DOI

  • Dissipative structure for symmetric hyperbolic systems with memory

    S. Kawashima, S. Taniue

    Sci. China Math.   61   137 - 150  2018

    DOI

  • Viscous shock profile and singular limit for hyperbolic systems with Cattaneo's law

    Tohru Nakamura, Shuichi Kawashima

    Kinetic and Related Models   11 ( 4 ) 795 - 819  2018

     View Summary

    In the current paper, we consider large time behavior of solutions to scalar conservation laws with an artificial heat flux term. In the case where the heat flux is governed by Fourier's law, the equation is scalar viscous conservation laws. In this case, existence and asymptotic stability of one-dimensional viscous shock waves have been studied in several papers. The main concern in the current paper is a 2 × 2 system of hyperbolic equations with relaxation which is derived by prescribing Cattaneo's law for the heat flux. We consider the one-dimensional Cauchy problem for the system of Cattaneo-type and show existence and asymptotic stability of viscous shock waves. We also obtain the convergence rate by utilizing the weighted energy method. By letting the relaxation time zero in the system of Cattaneo-type, the system is formally deduced to scalar viscous conservation laws of Fourier-type. This is a singular limit problem which occurs an initial layer. We also consider the singular limit problem associated with viscous shock waves.

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  • Global solutions to the equation of thermoelasticity with fading memory

    Mari Okada, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   263 ( 1 ) 338 - 364  2017.07  [Refereed]

     View Summary

    We consider the initial-history value problem for the one-dimensional equation of thermoelasticity with fading memory. It is proved that if the data are smooth and small, then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity. Our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels. (C) 2017 Elsevier Inc. All rights reserved.

    DOI

  • Decay structure of two hyperbolic relaxation models with regularity loss

    Yoshihiro Ueda, Renjun Duan, Shuichi Kawashima

    KYOTO JOURNAL OF MATHEMATICS   57 ( 2 ) 235 - 292  2017.06  [Refereed]

     View Summary

    This article investigates two types of decay structures for linear symmetric hyperbolic systems with nonsymmetric relaxation. Previously, the same authors introduced a new structural condition which is a generalization of the classical Kawashima-Shizuta condition and also analyzed the weak dissipative structure called the regularity loss type for general systems with nonsymraetric relaxation, which includes the Timoshenko system and the Euler-Maxwell system as two concrete examples. Inspired by the previous work, we further construct in this article two more complex models which satisfy some new decay structure of regularity-loss type. The proof is based on the elementary Fourier energy method as well as the suitable linear combination of different energy inequalities. The results show that the model of type I has a decay structure similar to that of the Timoshenko system with heat conduction via the Cattaneo law, and the model of type II is a direct extension of two models considered previously to the case of higher phase dimensions.

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  • The frequency-localization technique and minimal decay-regularity for Euler-Maxwell equations

    Jiang Xu, Shuichi Kawashima

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   446 ( 2 ) 1537 - 1554  2017.02  [Refereed]

     View Summary

    Dissipative hyperbolic systems of regularity-loss have been recently received increasing attention. Extra higher regularity is usually assumed to obtain the optimal decay estimates, in comparison with the global-in-time existence of solutions. In this paper, we develop a new frequency-localization time-decay property, which enables us to overcome the technical difficulty and improve the minimal decay-regularity for dissipative systems. As an application, it is shown that the optimal decay rate of L-1(R-3)-L-2(R-3) is available for Euler-Maxwell equations with the critical regularity s(c) = 5/2, that is, the extra higher regularity is not necessary. (C) 2016 Elsevier Inc. All rights reserved.

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  • A survey on global existence and time-decay estimates for hyperbolic system with dissipation

    J. Xu, S. Kawashima

    Advances in Mathematics (China)   46   321 - 330  2017

  • Discrete kinetic theory and hyperbolic balance laws

    S. Kawashima

    RIMS Kokyuroku Bessatsu "Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics"   67   123 - 135  2017

  • The minimal decay regularity of smooth solutions to the Euler-Maxwell two-fluid system

    Jiang Xu, Shuichi Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   13 ( 4 ) 719 - 733  2016.12  [Refereed]

     View Summary

    The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R-3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of L-p(R-n)-L-q(Rn)-L-r(R-n) time-decay estimates, we obtain the L-1(R-3)-L-2(R-3) decay rate with the critical regularity (s(c) = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Lineaire 29 (2012) 737-759].

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  • Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems in low dimensions

    Jiang Xu, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   261 ( 5 ) 2670 - 2701  2016.09  [Refereed]

     View Summary

    Recently, a time-decay framework L-2(R-n) boolean AND (B)over dot(2,infinity)(-s) (s > 0) has been given by [49] for linearized dissipative hyperbolic systems, which allows to pay, less attention to the traditional spectral analysis. However, owing to interpolation techniques, those decay results for nonlinear hyperbolic systems hold true only in higher dimensions (n >= 3), and the analysis in low dimensions (say, n = 1,2) was left open. We try to give a satisfactory Answer in the current work. First of all, we develop new time-decay properties on the frequency-localization Duhamel principle, and then it is-shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n = 1,2, by using a new technique which is the so-called "piecewise Duhamel principle" in localized time-weighted energy approaches compared to [49]. Finally, as direct applications, explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure, for instance, damped compressible Euler equations, the thermoelasticity with second sound, and Timoshenko systems with equal wave speeds. (C) 2016 Elsevier Inc. All rights reserved.

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  • Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space

    Yoshihiro Ueda, Shuichi Kawashima

    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY   47 ( 2 ) 787 - 797  2016.06  [Refereed]

     View Summary

    In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R-3. It is known in the authors' previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method.

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  • Decay property of the Timoshenko-Cattaneo system

    Naofumi Mori, Shuichi Kawashima

    ANALYSIS AND APPLICATIONS   14 ( 3 ) 393 - 413  2016.05  [Refereed]

     View Summary

    We study the Timoshenko system with Cattaneo's type heat conduction in the one-dimensional whole space. We investigate the dissipative structure of the system and derive the optimal L-2 decay estimate of the solution in a general situation. Our decay estimate is based on the detailed pointwise estimate of the solution in the Fourier space. We observe that the decay property of our Timoshenko-Cattaneo system is of the regularity-loss type. This decay property is a little different from that of the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Models Methods Appl. Sci. 18 (2008) 647-667]) in the low frequency region. However, in the high frequency region, it is just the same as that of the Timoshenko-Fourier system (see [N. Mori and S. Kawashima, Decay property for the Timoshenko system with Fourier's type heat conduction, J. Hyperbolic Differential Equations 11 (2014) 135-157]) or the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Models Methods Appl. Sci. 18 (2008) 647-667]), although the stability number is different. Finally, we study the decay property of the Timoshenko system with the thermal effect of memory-type by reducing it to the Timoshenko-Cattaneo system.

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  • Mathematical entropy and Euler-Cattaneo-Maxwell system

    Shuichi Kawashima, Yoshihiro Ueda

    ANALYSIS AND APPLICATIONS   14 ( 1 ) 101 - 143  2016.01  [Refereed]

     View Summary

    In this paper, we introduce a notion of the mathematical entropy for hyperbolic systems of balance laws with (not necessarily symmetric) relaxation. As applications, we deal with the Timoshenko system, the Euler-Maxwell system and the Euler-Cattaneo-Maxwell system. Especially, for the Euler-Cattaneo-Maxwell system, we observe that its dissipative structure is of the regularity-loss type and investigate the corresponding decay property. Furthermore, we prove the global existence and asymptotic stability of solutions to the Euler-Cattaneo-Maxwell system for small initial data.

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  • Global existence and minimal decay regularity for the Timoshenko system: The case of non-equal wave speeds

    Jiang Xu, Naofumi Mori, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   259 ( 11 ) 5533 - 5553  2015.12  [Refereed]

     View Summary

    As a continued work of 1181, we are concerned with the Timoshenko system in the case of non-equal wave speeds, which admits the dissipative structure of regularity-loss. Firstly, with the modification of a priori estimates in 1181, we construct global solutions to the Timoshenko system pertaining to data in the Besov space with the regularity s = 3/2. Owing to the weaker dissipative mechanism, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions, so it is almost impossible to obtain the optimal decay rates in the critical space. To overcome the outstanding difficulty, we develop a new frequency-localization time-decay inequality, which captures the information related to the integrability at the high-frequency part. Furthermore, by the energy approach in terms of high-frequency and low-frequency decomposition, we show the optimal decay rate for Timoshenko system in critical Besov spaces, which improves previous works greatly. (C) 2015 Elsevier Inc. All rights reserved.

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  • L-p-L-q-L-r estimates and minimal decay regularity for compressible Euler-Maxwell equations

    Jiang Xu, Naofumi Mori, Shuichi Kawashima

    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES   104 ( 5 ) 965 - 981  2015.11  [Refereed]

     View Summary

    Due to the dissipative structure of regularity-loss, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of this paper is to seek the lowest regularity index for the optimal decay rate of L-1(R-n)-L-2(R-n). Consequently, a notion of minimal decay regularity for dissipative systems of regularity-loss is firstly proposed. To do this, we develop a new time-decay estimate of L-p(R-n)-L-q(R-n)-L-r(R-n) type by using the low-frequency and high-frequency analysis in Fourier spaces. As an application, for compressible Euler-Maxwell equations with the weaker dissipative mechanism, it is shown that the minimal decay regularity coincides with the critical regularity for global classical solutions. Moreover, the recent decay property for symmetric hyperbolic systems with non-symmetric dissipation is also extended to be the L-p-version. (C) 2015 Elsevier Masson SAS. All rights reserved.

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  • The Optimal Decay Estimates on the Framework of Besov Spaces for Generally Dissipative Systems

    Jiang Xu, Shuichi Kawashima

    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   218 ( 1 ) 275 - 315  2015.10  [Refereed]

     View Summary

    We give a new decay framework for the general dissipative hyperbolic system and the hyperbolic-parabolic composite system, which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts. New ingredients lie in the high-frequency and low-frequency decomposition of a pseudo-differential operator and an interpolation inequality related to homogeneous Besov spaces of negative order. Furthermore, we develop the Littlewood-Paley pointwise energy estimates and new time-weighted energy functionals to establish optimal decay estimates on the framework of spatially critical Besov spaces for the degenerately dissipative hyperbolic system of balance laws. Based on the embedding and the improved Gagliardo-Nirenberg inequality, the optimal decay rates and decay rates are further shown. Finally, as a direct application, the optimal decay rates for three dimensional damped compressible Euler equations are also obtained.

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  • The optimal decay estimates on the framework of Besov spaces for the Euler-Poisson two-fluid system

    Jiang Xu, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   25 ( 10 ) 1813 - 1844  2015.09  [Refereed]

     View Summary

    In this paper, we are concerned with the optimal decay estimates for the Euler-Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta-Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of L-p(R-3)-L-2 (R-3) (1 <= p < 2) type for the Euler-Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler-Poisson equations, which leads to the sharp decay estimates for velocities.

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  • Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

    Shuichi Kawashima, Yu-Zhu Wang

    ANALYSIS AND APPLICATIONS   13 ( 3 ) 233 - 254  2015.05  [Refereed]

     View Summary

    In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n >= 1. Moreover, when n >= 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

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  • Global existence and optimal decay rates for the Timoshenko system: The case of equal wave speeds

    Naofumi Mori, Jiang Xu, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   258 ( 5 ) 1494 - 1518  2015.03  [Refereed]

     View Summary

    We first show the global existence and optimal decay rates of solutions to the classical Timoshenko system in the framework of Besov spaces. Due to the non-symmetric dissipation, the general theory for dissipative hyperbolic systems (see [31]) cannot be applied to the Timoshenko system directly. In the case of equal wave speeds, we construct global solutions to the Cauchy problem pertaining to data in the spatially Besov spaces. Furthermore, the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis. Consequently, the optimal decay estimates of solution and its derivatives of fractional order are shown by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As a by-product, the usual decay estimate of L-1 (R)-L-2 (R) type is also shown. (C) 2014 Elsevier Inc. All rights reserved.

    DOI

  • Mathematical analysis for systems of viscoelasticity and viscothermoelasticity, Proce edings on "Mathematical fluids Dynamics and Nonlinear Wave" (T. Kobayashi, S. Shimizu, Y. Enomoto and N. Yamaguchi,, eds), Gakuto International Series

    S. Kawashima

    Mathematical Sciences and Applications   37   105 - 134  2015

  • Global existence and optimal decay of solutions to the dissipative Timoshenko system, "Mathematical Analysis of Viscous Incompressible fluid"

    N. Mori, S. Kawashima

    RIMS Kokyuroku   1971   150 - 164  2015

  • Asymptotic profile of solutions to a hyperbolic Cahn-Hilliard equation

    H. Takeda, Y. Maekawa, S. Kawashima

    Bulletin of the Institute of Mathematics, Academia Sinica (New Series)   10   479 - 539  2015

  • Large time behavior of solutions to symmetric hyperbolic systems with non-symmetric relaxation, Nonlinear Dynamics in Partial Differential Equations

    Y. Ueda, R.-J. Duan, S. Kawashima

    Adv. Stud. Pure Math.   64   295 - 302  2015  [Refereed]

  • Dissipative structure of the coupl ed kineticfluid models, Nonlinear Dynamics in Partial Di?erential Equations

    R.-J. Duan, S. Kawashima, Y. Ueda

    Adv. Stud. Pure Math.   64   327 - 335  2015

  • Decay estimates of solutions for nonlinear viscoelastic systems, Nonlinear Dynamics in Partial Differential Equations

    P.M.N. Dharmawardane, T. Nakamura, S. Kawashima

    Adv. Stud. Pure Math.   64   377 - 385  2015  [Refereed]

  • Global existence and asymptotic decay of solutions to the non-isentropic Euler-Maxwell system

    Yue-Hong Feng, Shu Wang, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   24 ( 14 ) 2851 - 2884  2014.12  [Refereed]

     View Summary

    The non-isentropic compressible Euler-Maxwell system is investigated in R-3 in this paper, and the L-q time decay rate for the global smooth solution is established. It is shown that the density and temperature of electron converge to the equilibrium states at the same rate (1 + t)(-11/4) in L-q norm. This phenomenon on the charge transport shows the essential relation of the equations with the non-isentropic Euler-Maxwell and the isentropic Euler-Maxwell equations.

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  • DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH FOURIER'S TYPE HEAT CONDUCTION

    Naofumi Mori, Shuichi Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   11 ( 1 ) 135 - 157  2014.03  [Refereed]

     View Summary

    We study the Timoshenko system with Fourier's type heat conduction in the one-dimensional (whole) space. We observe that the dissipative structure of the system is of the regularity-loss type, which is somewhat different from that of the dissipative Timoshenko system studied earlier by Ide-Haramoto-Kawashima. Moreover, we establish optimal L-2 decay estimates for general solutions. The proof is based on detailed pointwise estimates of solutions in the Fourier space. Also, we introuce here a refinement of the energy method employed by Ide-Haramoto-Kawashima for the dissipative Timoshenko system, which leads us to an improvement on their energy method.

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  • Global classical solutions for partially dissipative hyperbolic systems of balance laws

    J. Xu, S. Kawashima

    Arch. Rat. Mech. Anal.   211   513 - 553  2014  [Refereed]

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  • Diffusive relaxation limit of classical solutions to the damped compressible Euler equations

    Jiang Xu, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   256 ( 2 ) 771 - 796  2014.01  [Refereed]

     View Summary

    We construct (uniform) global classical solutions to the damped compressible Euler equations on the framework of general Besov spaces which includes both the usual Sobolev spaces H-s (R-d) (s > 1 + d/2) and the critical Besov space B-2,1(1+d/2) (R-d). Such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous Chemin-Lerner spaces. Furthermore, we obtain the diffusive relaxation limit of Euler equations towards the porous medium equation, by means of Aubin-Lions compactness argument. (C) 2013 Elsevier Inc. All rights reserved.

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  • ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION IN ONE SPACE DIMENSION

    Masakazu Kato, Yu-Zhu Wang, Shuichi Kawashima

    KINETIC AND RELATED MODELS   6 ( 4 ) 969 - 987  2013.12  [Refereed]

     View Summary

    We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition.

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  • Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory

    Yongqin Liu, Shuichi Kawashima

    Nonlinear Analysis, Theory, Methods and Applications   84   1 - 17  2013

     View Summary

    In this paper we consider the initial-value problem for the nonlinear Timoshenko system with a memory term. Due to the regularity-loss property and weak dissipation, we have to assume stronger nonlinearity than usual. By virtue of the semi-group arguments, we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data, where we employ a time-weighted L2 energy method combined with the optimal L2 decay of lower-order derivatives of solutions. © 2013 Elsevier Ltd. All rights reserved.

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  • Global well-posedness in critical besov spaces for two-fluid euler-maxwell equations

    Jiang Xu, Jun Xiong, Shuichi Kawashima

    SIAM Journal on Mathematical Analysis   45 ( 3 ) 1422 - 1447  2013

     View Summary

    In this paper, we study two-fluid compressible Euler-Maxwell equations in the whole space or periodic space. In comparison with the one-fluid case, we need to deal with the difficulty mainly caused by the nonlinear coupling and cancelation between electrons and ions. Precisely, the expected dissipation rates of densities for two carriers are no longer available. To capture the weaker dissipation, we develop a continuity for compositions, which is a natural generalization from Besov spaces to Chemin-Lerner spaces (space-time Besov spaces). An elementary fact that indicates the relation between homogeneous Chemin-Lerner spaces and inhomogeneous Chemin-Lerner spaces will been also used. © 2013 Society for Industrial and Applied Mathematics.

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  • ASYMPTOTIC STABILITY OF STATIONARY SOLUTIONS TO THE DRIFT-DIFFUSION MODEL IN THE WHOLE SPACE

    Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima

    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS   18 ( 4 ) 1097 - 1121  2012.10  [Refereed]

     View Summary

    We study the initial value problem for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We show that the corresponding stationary problem in the whole space R-n admits a unique stationary solution in a general situation. Moreover, it is proved that when n >= 3, a unique solution to the initial value problem exists globally in time and converges to the corresponding stationary solution as time tends to infinity, provided that the amplitude of the stationary solution and the initial perturbation are suitably small. Also, we show the sharp decay estimate for the perturbation. The stability proof is based on the time weighted L-p energy method.

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  • DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

    Yongqin Liu, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   22 ( 2 ) 1 - 19  2012.02  [Refereed]

     View Summary

    In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier-Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

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  • The initial value problem for some hyperbolic-dispersive system

    Shuichi Kawashima, Chi-Kun Lin, Jun-ichi Segata

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES   35 ( 2 ) 125 - 133  2012.01  [Refereed]

     View Summary

    We consider the initial value problem for some nonlinear hyperbolic-dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system. Copyright (C) 2011 John Wiley & Sons, Ltd.

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  • Decay structure for symmetric hyperbolic systems with non-symmetric relaxation, its applications

    Y. Ueda, R.-J. Duan, S. Kawashima

    Arch. Rat. Mech. Anal.   205   239 - 266  2012  [Refereed]

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  • DECAY ESTIMATES OF SOLUTIONS FOR QUASI-LINEAR HYPERBOLIC SYSTEMS OF VISCOELASTICITY

    Priyanjana M. N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   44 ( 3 ) 1976 - 2001  2012  [Refereed]

     View Summary

    This paper is devoted to the study of the sharp decay estimates of solutions for quasi-linear hyperbolic systems of viscoelasticity in the whole space. We develop the time-weighted energy method for our system, which can yield the decay estimate of solutions for small initial data in L-2, provided that n >= 2. Also, we discuss the fundamental solutions to the linearized system and study the decay properties for the corresponding solution operators. Then, by employing the same time-weighted energy method together with the semigroup argument, we show the optimal decay estimate of solutions for small initial data in L-2 boolean AND L-1 and for all n >= 1.

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  • DISSIPATIVE STRUCTURE OF THE REGULARITY-LOSS TYPE AND TIME ASYMPTOTIC DECAY OF SOLUTIONS FOR THE EULER-MAXWELL SYSTEM

    Yoshihiro Ueda, Shu Wang, Shuichi Kawashima

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   44 ( 3 ) 2002 - 2017  2012  [Refereed]

     View Summary

    We consider the large-time behavior of solutions to the initial value problem for the Euler-Maxwell system in R-3. This system verifies the decay property of the regularity-loss type. Under smallness condition on the initial perturbation, we show that the solution to the problem exists globally in time and converges to the equilibrium state as time tends to infinity. The crucial point of the proof is to derive a priori estimates of solutions by using the energy method.

    DOI

  • GLOBAL EXISTENCE AND DECAY OF SOLUTIONS FOR A QUASI-LINEAR DISSIPATIVE PLATE EQUATION

    Yongqin Liu, Shuichi Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   8 ( 3 ) 591 - 614  2011.09  [Refereed]

     View Summary

    In this paper we focus on the initial value problem of a quasi-linear dissipative plate equation with arbitrary spatial dimensions (n >= 1). This equation verifies the decay property of the regularity-loss type. To overcome the difficulty caused by the regularity-loss property, we employ a special time-weighted (with negative exponent) L(2) energy method combined with the optimal L(2) decay estimates of lower-order derivatives of solutions. We obtain the global existence and optimal decay estimates of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is the fundamental solution of the corresponding fourth-order linear parabolic equation.

    DOI

  • Global solutions to quasi-linear hyperbolic systems of viscoelasticity

    Priyanjana M. N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima

    Kyoto Journal of Mathematics   51 ( 2 ) 467 - 483  2011.06

     View Summary

    In the present paper, we study a large-time behavior of solutions to a quasilinear second-order hyperbolic system which describes a motion of viscoelastic materials. The system has dissipative properties consisting of a memory term and a damping term. It is proved that the solution exists globally in time in the Sobolev space, provided that the initial data are sufficiently small. Moreover, we show that the solution converges to zero as time tends to infinity. The crucial point of the proof is to derive uniform a priori estimates of solutions by using an energy method. © 2011 by Kyoto University.

    DOI

  • DECAY PROPERTY FOR A PLATE EQUATION WITH MEMORY-TYPE DISSIPATION

    Yongqin Liu, Shuichi Kawashima

    KINETIC AND RELATED MODELS   4 ( 2 ) 531 - 547  2011.06  [Refereed]

     View Summary

    In this paper we focus on the initial value problem of the semi-linear plate equation with memory in multi-dimensions (n >= 1), the decay structure of which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain the fundamental solutions and thus the solution to the corresponding linear problem. Appealing to the point-wise estimate in the Fourier space of solutions to the linear problem, we get estimates and properties of solution operators, by exploiting which decay estimates of solutions to the linear problem are obtained. Also by introducing a set of time-weighted Sobolev spaces and using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.

    DOI

  • Time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity

    Priyanjana M. N. Dharmawardane, Tohru Nakamura, Shuichi Kawashima

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   87 ( 6 ) 99 - 102  2011.06  [Refereed]

     View Summary

    The aim in this paper is to develop the time-weighted energy method for quasilinear hyperbolic systems of viscoelasticity. As a consequence, we prove the global existence and decay estimate of solutions for the space dimension n >= 2; provided that the initial data are small in the L-2-Sobolev space.

    DOI

  • TRAVELING WAVES FOR MODELS OF PHASE TRANSITIONS OF SOLIDS DRIVEN BY CONFIGURATIONAL FORCES

    Shuichi Kawashima, Peicheng Zhu

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   15 ( 1 ) 309 - 323  2011.01  [Refereed]

     View Summary

    This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transitions of solid materials, e.g., Steel, and phase transitions due to interface motion by interface diffusion, e.g., Sintering. These models were proposed by Alber and Zhu in [3]. We consider both the order-parameter-conserved case and the non-conserved one, under suitable assumptions. Also we compare our results with the corresponding ones for the Allen-Cahn and the Cahn-Hilliard equations coupled with linear elasticity, which are models for diffusion-dominated phase transitions in elastic solids.

    DOI

  • Global existence, asymptotic behavior of solutions for quasi-linear dissipative plate equation

    Y. Liu, S. Kawashima

    Discrete Continuous Dynamical Systems   39   1113 - 1139  2011  [Refereed]

  • ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF A RADIATING GAS

    Yongqin Liu, Shuichi Kawashima

    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   10 ( 1 ) 209 - 223  2011.01  [Refereed]

     View Summary

    In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates of solutions. Moreover, we show that the solution is asymptotic to the linear diffusion wave which is given in terms of the heat kernel.

    DOI

  • Energy method in the partial Fourier space and application to stability problems in the half space

    Yoshihiro Ueda, Tohru Nakamura, Shuichi Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   250 ( 2 ) 1169 - 1199  2011.01  [Refereed]

     View Summary

    The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space R-n. In this paper, we study half space problems in R-+(n) = R+ x Rn-1 and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x' is an element of Rn-1. For the variable x(i) is an element of R+ in the normal direction, we use L-2 space or weighted L-2 space. We apply this energy method to the half space problem for damped wave equations with a nonlinear convection term and prove the asymptotic stability of planar stationary waves by showing a sharp convergence rate for t -> infinity. The result obtained in this paper is a refinement of the previous one in Ueda et al. (2008) [13]. (C) 2010 Elsevier Inc. All rights reserved.

    DOI

  • Decay structure for systems of viscoelasticity, Proce edings of the International Conference "Mathematical Analysis on the Navier-Stokes equations, Relat ed Topics, Past, Future in memory of Professor Tetsuro Miyakawa"

    S. Kawashima

    Math. Sci. Appl.   35   91 - 102  2011

  • Decay property of regularity-loss type for the EulerMaxwell system

    Y. Ueda, S. Kawashima

    Methods, Applications of Analysis   18   245 - 268  2011

    DOI

  • Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate

    Shuichi Kawashima, Tohru Nakamura, Shinya Nishibata, Peicheng Zhu

    Mathematical Models and Methods in Applied Sciences   20 ( 12 ) 2201 - 2235  2010.12

     View Summary

    The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method. © 2010 World Scientific Publishing Company.

    DOI

  • DECAY ESTIMATES OF SOLUTIONS TO A SEMI-LINEAR DISSIPATIVE PLATE EQUATION

    Yousuke Sugitani, Shuichi Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   7 ( 3 ) 471 - 501  2010.09  [Refereed]

     View Summary

    We study the initial value problem for a semi-linear dissipative plate equation in n-dimensional space. We observe that the dissipative structure of the linearized equation is of the regularity-loss type. This means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data. This regularity-loss property causes the difficulty in solving the nonlinear problem. For our semi-linear problem, this difficulty can be overcome by introducing a set of time-weighted Sobolev spaces, where the time-weights and the regularity of the Sobolev spaces are determined by our regularity-loss property. Consequently, under smallness condition on the initial data, we prove the global existence and optimal decay of the solution in the corresponding Sobolev spaces.

    DOI

  • Decay property for second order hyperbolic systems of viscoelastic materials

    Priyanjana M. N. Dharmawardane, Jaime E. Munoz Rivera, Shuichi Kawashima

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   366 ( 2 ) 621 - 635  2010.06  [Refereed]

     View Summary

    We study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials. The considered dissipation is given by the sum of the memory term and the damping term. When the dissipation is effective over the whole system, we show that the solution decays in L(2) at the rate t(-n/4) as t ->infinity provided that the corresponding initial data are in L(2) boolean AND L(1). where n is the space dimension. The proof is based on the energy method in the Fourier space. Also, we discuss similar systems with weaker dissipation by introducing the operator (1 - Delta)(-theta/2) with theta > 0 in front of the dissipation terms and observe that the decay structure of these systems is of the regularity-loss type. (C) 2009 Elsevier Inc. All rights reserved.

    DOI

  • Stability of degenerate stationary waves for viscous gases

    Y. Ueda, T. Nakamura, S. Kawashima

    Arch. Rat. Mech. Anal.   198   735 - 762  2010

    DOI

  • Convergence rate toward degenerate stationary wave for compressible viscous gases, Proce edings of the 6th International Conference on Nonlinear Analysis, Convex Analysis (Tokyo, Japan, 2009)

    T. Nakamura, Y. Ueda, S. Kawashima

    Yokohama Publ.     239 - 248  2010

  • Decaying solution of the Navier-Stokes flow of infinite volume without surface tension

    Yasushi Hataya, Shuichi Kawashima

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   71 ( 12 ) E2535 - E2539  2009.12  [Refereed]

     View Summary

    In this short paper, we report global existence and temporal decay properties for the solution of theNavier-Stokes equations with free boundary, describing the motion of infinite mass of viscous, incompressible fluid without surface tension. (C) 2009 Elsevier Ltd. All rights reserved.

    DOI

  • Asymptotic Stability of Rarefaction Wave for the Navier-Stokes Equations for a Compressible Fluid in the Half Space

    Shuichi Kawashima, Peicheng Zhu

    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   194 ( 1 ) 105 - 132  2009.10  [Refereed]

     View Summary

    This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes equations in a compressible fluid in the Eulerian coordinate in the half space. This is the second one of our series of papers on this subject. In this paper, firstly we classify completely the time-asymptotic states, according to some parameters, that is the spatial-asymptotic states and boundary conditions, for this initial boundary value problem, and some pictures for the classification of time-asymptotic states are drawn in the state space. In order to prove the stability of the rarefaction wave, we use the solution to Burgers' equation to construct a suitably smooth approximation of the rarefaction wave and establish some time-decay estimates in L (p) -norm for the smoothed rarefaction wave. We then employ the L (2)-energy method to prove that the rarefaction wave is non-linearly stable under a small perturbation, as time goes to infinity.

    DOI

  • Hardy type inequality and application to the stability of degenerate stationary waves

    Shuichi Kawashima, Kazuhiro Kurata

    JOURNAL OF FUNCTIONAL ANALYSIS   257 ( 1 ) 1 - 19  2009.07  [Refereed]

     View Summary

    This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous conservation laws in the half space. It is proved that the solution converges to the corresponding degenerate stationary wave at the rate t(-alpha/4) as t -> infinity, provided that the initial perturbation is in the weighted space L(alpha)(2) = L(2)(R(+); (1 + x)(alpha)) for alpha < alpha(c)(q) := 3 + 2/q, where q is the degeneracy exponent. This restriction on a is best possible in the sense that the corresponding linearized operator cannot be dissipative in L(alpha)(2) for alpha > alpha(c)(q). Our stability analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant. (c) 2009 Elsevier Inc. All rights reserved.

    DOI

  • Stationary solutions to the drift-diffusion model in the whole spaces

    Ryo Kobayashi, Masaki Kurokiba, Shuichi Kawashima

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES   32 ( 6 ) 640 - 652  2009.04  [Refereed]

     View Summary

    We study the stationary problem in the whole space R(n) for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We prove the existence and uniqueness of stationary solutions in the weighted LP spaces. The proof is based on a fixed point theorem of the Leray-Schauder type. Copyright (C) 2008 John Wiley & Sons, Ltd.

    DOI

  • Decay estimates for hyperbolic balance laws

    S. Kawashima, W.-A. Yong

    ZAA (J. Anal. Appl.)   28   1 - 33  2009  [Refereed]

    DOI

  • Decay property of regularity-loss type, nonlinear effects for some hyperbolic-elliptic system

    T. Kubo, S. Kawashima

    Kyushu J. Math.   63   1 - 21  2009  [Refereed]

    DOI

  • Stability of planar stationary waves for damp ed wave equations with nonlinear convection in half space, Hyperbolic Problems: Theory, Numerics, Applications, (E. Tadmor, J.-G. Liu and A. Tzavaras,, eds)

    Y. Ueda, T. Nakamura, S. Kawashima

    Proce edings of Symposia in Appli ed Mathematics   67   977 - 986  2009

    DOI

  • 緩和的双曲型保存則系の数学解析

    川島秀一

    雑誌「数学」61巻3号     248 - 269  2009

  • Convergence rate to the nonlinear waves for viscous conservation laws on the half line

    I. Hashimoto, Y. Ueda, S. Kawashima

    Methods, Applications of Analysis   16   389 - 402  2009

    DOI

  • Decay Estimates and Large Time Behavior of Solutions to the Drift-Diffusion System

    Ryo Kobayashi, Shuichi Kawashima

    FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA   51 ( 3 ) 371 - 394  2008.12  [Refereed]

     View Summary

    We Study the drift-diffusion system arising in the semiconductor device simulation and the plasma physics. We consider the initial value problem for this system and derive the optimal L(P) decay estimate of solutions by applying the time weighted L(P) energy method. Furthermore, we show that the solutions approach the corresponding heat kernels as time tends to infinity. This asymptotic result is based on the optimal L(P) - L(q) decay estimate for the linearized problem.

    DOI

  • Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system

    Kentaro Ide, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   18 ( 7 ) 1001 - 1025  2008.07

     View Summary

    We consider the initial value problem for a nonlinear version of the dissipative Timoshenko system. This syetem verifies the decay property of regularity-loss type. To overcome this difficulty caused by the regularity-loss property, we employ the time weighed L-2 energy method which is combined with the optimal L-2 decay estimates for lower order derivatives of solutions. Then we show the global existence and asymptotic decay of solutions under smallness and enough regularity conditions on the initial data. Moreover, we show that the solution approaches the linear diffusion wave expressed in terms of the superposition of the heat kernels as time tends to infinity.

    DOI

  • Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space

    Shuichi Kawashima, Peicheng Zhu

    JOURNAL OF DIFFERENTIAL EQUATIONS   244 ( 12 ) 3151 - 3179  2008.06  [Refereed]

     View Summary

    In the present paper, we investigate the large-time behavior of the solution to an initial-boundary value problem for the isentropic compressible Navier-Stokes equations in the Eulerian coordinate in the half space. This is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible Navier-Stokes equations. Some suitable assumptions are made to guarantee that the time-asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L-2-energy method and making use of the techniques from the paper [S. Kawashima, Y. Nikkuni, Stability of rarefaction waves for the discrete Boltzmann equations, Adv. Math. Sci. Appl. 12 (1) (2002) 327-353], we prove that this nonlinear wave is nonlinearly stable under a small perturbation. The complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates, however those terms are of two basic types, and the terms of each type are "good" and can be evaluated suitably by using the decay (in both time and space variables) estimates of each component of nonlinear wave. (c) 2008 Elsevier Inc. All rights reserved.

    DOI

  • Decay property of regularity-loss type for dissipative Timoshenko system

    Kentaro Ide, Kazuo Haramoto, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   18 ( 5 ) 647 - 667  2008.05  [Refereed]

     View Summary

    We study the decay property of the dissipative Timoshenko system in the one-dimensional whole space. We derive the L-2 decay estimates of solutions in a general situation and observe that this decay structure is of the regularity-loss type. Also, we give a refinement of these decay estimates for some special initial data. Moreover, under enough regularity assumption on the initial data, we show that the solution approaches the linear diffusion wave expressed in terms of the heat kernels as time tends to infinity. The proof is based on the detailed pointwise estimates of solutions in the Fourier space.

    DOI

  • Dissipative structure of regularity-loss type, applications, Hyperbolic Problems: Theory, Numerics, Applications (S. Benzoni-Gavage, D. Serre, eds)

    S. Kawashima

    Springer-Verlag     45 - 57  2008

  • Stability of planar stationary waves for damp ed wave equations with nonlinear convection in multi-dimensional half space

    Y. Ueda, T. Nakamura, S. Kawashima

    Kinetic, Relat ed Models   1   49 - 64  2008

    DOI

  • Large time behavior of solutions to a semilinear hyperbolic system with relaxation

    Yoshihiro Ueda, Shuichi Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   4 ( 1 ) 147 - 179  2007.03  [Refereed]

     View Summary

    We are concerned with the initial value problem for a damped wave equation with a nonlinear convection term which is derived from a semilinear hyperbolic system with relaxation. We show the global existence and asymptotic decay of solutions in W-1,W-p (1 <= p <= infinity) under smallness condition on the initial data. Moreover, we show that the solution approaches in W-1,W-p (1 <= p <= infinity) the nonlinear diffusion wave expressed in terms of the self-similar solution of the Burgers equation as time tends to infinity. Our results are based on the detailed pointwise estimates for the fundamental solutions to the linearlized equation.

    DOI

  • Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system

    Takafumi Hosono, Shuichi Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   16 ( 11 ) 1839 - 1859  2006.11  [Refereed]

     View Summary

    We discuss the global solvability and asymptotic behavior of solutions to the Cauchy problem for some nonlinear hyperbolic-elliptic system with a fourth-order elliptic part. This system is a modified version of the simplest radiating gas model and verifies a decay property of regularity-loss type. Such a dissipative structure also appears in the dissipative Timoshenko system studied by Rivera and Racke. This dissipative property is very weak in high frequency region and causes the difficulty in deriving the desired a priori estimates for global solutions to the nonlinear problem. In fact, it turns out that the usual energy method does not work well. We overcome this difficulty by employing a time-weighted energy method which is combined with the optimal decay for lower order derivatives of solutions, and we establish a global existence and asymptotic decay result. Furthermore, we show that the solution has an asymptotic self-similar profile described by the Burgers equation as time tends to infinity.

    DOI

  • Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

    Yoshiyuki Kagei, Shuichi Kawashima

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   266 ( 2 ) 401 - 430  2006.09  [Refereed]

     View Summary

    Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space R-+(n)(n >= 2) under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in H-s (R-+(n)) with s >= [n/2] + 1 and the perturbations decay in L-infinity norm as t --> infinity, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

    DOI

  • Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system

    Y Kagei, S Kawashima

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   3 ( 2 ) 195 - 232  2006.06  [Refereed]

     View Summary

    This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in H-s, where s is an integer satisfying s >= [n/2] + 1.

    DOI

  • Dissipative structure and entropy for hyperbolic systems of balance laws

    S Kawashima, WA Yong

    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   174 ( 3 ) 345 - 364  2004.12  [Refereed]

     View Summary

    In this paper, we introduce an entropy condition for hyperbolic systems of balance laws. Under this condition, we use the Chapman-Enskog expansion to derive the corresponding viscous conservation laws. Further structural conditions are discussed in order to develop (local and global) existence theories for the balance laws and viscous conservation laws.

    DOI

  • L-p energy method for multi-dimensional viscous conservation laws and application to the stability of planar waves

    S Kawashima, S Nishibata, M Nishikawa

    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS   1 ( 3 ) 581 - 603  2004.09  [Refereed]

     View Summary

    We introduce a new L-p energy method for multi-dimensional viscous conservation laws. Our energy method is useful enough to derive the optimal decay estimates of solutions in the W-1,W-p space for the Cauchy problem. It is also applicable to the problem for the stability of planar waves in the whole space or in the half space, and gives the optimal convergence rate toward the planar waves as time goes to infinity. This energy method makes use of several special interpolation inequalities.

    DOI

  • Stability of rarefaction waves for a model system of a radiating gas

    Shuichi Kawashima, Yoshohito Tanaka

    Kyushu Journal of Mathematics   58 ( 2 ) 211 - 250  2004

    DOI

  • Large-time behavior of solutions to hyperbolic-elliptic coupled systems

    S Kawashima, Y Nikkuni, S Nishibata

    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   170 ( 4 ) 297 - 329  2003.12  [Refereed]

     View Summary

    We are concerned with the asymptotic behavior of a solution to the initial value problem for a system of hyperbolic conservation laws coupled with elliptic equations. This kind of problem was first considered in our previous paper. In the present paper, we generalize the previous results to a broad class of hyperbolic-elliptic coupled systems.
    Assuming the existence of the entropy function and the stability condition, we prove the global existence and the asymptotic decay of the solution for small initial data in a suitable Sobolev space. Then, it is shown that the solution is well approximated, for large time, by a solution to the corresponding hyperbolic-parabolic coupled system. The first result is proved by deriving a priori estimates through the standard energy method. The spectral analysis with the aid of the a priori estimate gives the second result.

    DOI

  • Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space

    S Kawashima, S Nishibata, PC Zhu

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   240 ( 3 ) 483 - 500  2003.09  [Refereed]

     View Summary

    We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier-Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L-2-energy method with the aid of the Poincare type inequality.

    DOI

  • ASYMPTOTIC STABILITY OF STATIONARY WAVES FOR TWO-DIMENSIONAL VISCOUS CONSERVATION LAWS IN HALF PLANE

    Shuichi Kawashima, Shinya Nishibata, Masataka Nishikawa

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS     469 - 476  2003  [Refereed]

     View Summary

    We investigate the asymptotic stability of a stationary solution to an initial boundary value problem for a 2-dimensional viscous conservation law in half plane. Precisely, we show that under suitable boundary and spatial asymptotic conditions, a solution converges to the corresponding stationary solution as time tends to infinity. The proof is based on an a priori estimate in the H-2-Sobolev space, which is obtained by a standard energy method. In this computation, we utilize the Poincare type inequality. In addition, we obtain a convergence rate under the assumption that the initial data converges to a spatial asymptotic state algebraically fast. This result is obtained by a weighted energy estimate.

  • On space-time decay properties of solutions to hyperbolicelliptic coupled systems

    T. Iguchi, S. Kawashima

    Hiroshima Math. J.   32   229 - 308  2002

  • Asymptotic stability of rarefaction waves for some discrete velocity model of the Boltzmann equation in the half-space

    Y. Nikkuni, S. Kawashima

    Adv. Math. Sci. Appl.   12   327 - 353  2002

  • A singular limit for hyperbolic-elliptic coupl ed systems in radiation hydrodynamics

    S. Kawashima, S. Nishibata

    Indiana Univ. Math. J.   50   567 - 589  2001

    DOI

  • Stationary waves for the discrete Boltzmann equations in the half space, Hyperbolic Problems: Theory, Numerics, Applications (H. Freistuühler and G. Warnecke, eds)

    S. Kawashima, S. Nishibata

    Birkhüauser   141   567 - 602  2001

  • Stability of stationary solutions to the half-space problem for the discrete boltzmann equation with multiple collisions

    Yoshiko Nikkuni, Shuichi Kawashima

    Kyushu Journal of Mathematics   54 ( 2 ) 233 - 255  2000

    DOI

  • Stationary waves for the discrete Boltzmann equation in the half space with reflective boundaries

    Shuichi Kawashima, Shinya Nishibata

    Communications in Mathematical Physics   211 ( 1 ) 183 - 206  2000

     View Summary

    The present paper is concerned with stationary solutions for discrete velocity models of the Boltzmann equation with reflective boundary condition in the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of stationary solutions satisfying the reflective boundary condition as well as the spatially asymptotic condition given by a Maxwellian state. First, the sufficient condition is obtained for the linearized system. Then, this result is applied to prove the existence theorem for the nonlinear equation through the contraction mapping principle. Also, it is shown that the stationary solution approaches the asymptotic Maxwellian state exponentially as the spatial variable tends to infinity. Moreover, we show the time asymptotic stability of the stationary solutions. In the proof, we employ the standard energy method to obtain a priori estimates for nonstationary solutions. The exponential convergence at the spatial asymptotic state of the stationary solutions gives essential information to handle some error terms. Then we discuss some concrete models of the Boltzmann type as an application of our general theory.

    DOI

  • Existence of a stationary wave for the discrete Boltzmann equation in the half space

    S Kawashima, S Nishibata

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   207 ( 2 ) 385 - 409  1999.11  [Refereed]

     View Summary

    We-study the existence and the uniqueness of stationary-solutions for discrete velocity models of the Boltzmann equation in the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of solutions-connecting the given boundary data and the Maxwellian state at a spatially asymptotic point. First, a sufficient condition is obtained for the Linearized system. Then this result as well as the contraction mapping principle is applied to prove the existence theorem for the nonlinear equation.
    Also, we show that the stationary wave approaches the Maxwellian state exponentially at a spatially asymptotic point. We also discuss some concrete models of Boltzmann type as an application of our general theory. Here, it turns out that our sufficient condition is general enough to cover many concrete models.

  • Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions

    S Kawashima, S Nishibata

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   9 ( 1 ) 69 - 91  1999.02  [Refereed]

     View Summary

    This paper deals with the global existence and the time asymptotic state of solutions to the initial value problems for the system derived from approximating a one-dimensional model of a radiating gas. When the spatial derivative of the initial data is larger than a certain negative critical value, a unique solution exists globally in time. But if it is smaller than another negative critical value, the spatial derivative of the corresponding solution blows up in a finite time. Thus it is natural to think about weak solutions in a suitable sense. As a prototype of weak solutions, we consider the Cauchy problem with the Riemann initial data of which the left state is larger than the right state. This condition ensures the existence of the corresponding traveling wave, connecting the left state and the right state asymptotically. This Riemann problem admits a global weak solution, provided that the magnitude of the initial discontinuity is smaller than 1/2. Although the solution has a discontinuity, we have the uniqueness of a solution in weak sense by imposing the entropy condition. Furthermore, the magnitude of the discontinuity contained in the solution decays to zero with an exponential rate as the time t goes to infinity. Also, the solution approaches the corresponding traveling wave with the rate t(-1/4) uniformly. The first result is obtained by the maximal principles. To show the second result, we have used an energy method with some estimates, which are also obtained through maximal principles.

  • Shock waves for a model system of the radiating gas

    S Kawashima, S Nishibata

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   30 ( 1 ) 95 - 117  1998.10  [Refereed]

     View Summary

    This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C-3-smooth traveling waves are asymptotically stable and that the rate of convergence toward these waves is t(?1/4),which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one.

  • Exponentially decaying component of a global solution to a reaction-diffusion system

    H Hoshino, S Kawashima

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   8 ( 5 ) 897 - 904  1998.08  [Refereed]

     View Summary

    A reaction-diffusion system which is related to a simple irreversible chemical reaction between two chemical substances is considered. When a non-negative global solution for the system converges uniformly to zero with polynomial rate as time goes to infinity, large-time approximation of the solution is studied. It is shown that the difference of the solution and its spatial average tends to zero with exponential rate via a global solution for the corresponding system of ordinary differential equations.

  • The initial value problem for hyperbolicelliptic coupl ed systems, applications to radiation hydrodynamics, Analysis of Systems of Conservation Laws (H. Freistühler, ed.)

    S. Kawashima, Y. Nikkuni, S. Nishibata

    Chapman & Hall/ CRC     87 - 127  1998

  • Smooth shock pro les in viscoelasticity with memory, Nonlinear Evolutionary Partial Differential Equations (X.-X. Ding and T.-P. Liu, eds)

    S. Kawashima, H. Hattori

    Studies in Advanced Mathematics   3   271 - 281  1997

  • Nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory

    H Hattori, S Kawashima

    JOURNAL OF DIFFERENTIAL EQUATIONS   127 ( 1 ) 174 - 196  1996.05  [Refereed]

     View Summary

    In this paper, we shall discuss the stability of smooth monotone travelling wave solutions for viscoelastic materials with memory. It is known that a smooth monotone travelling wave solution exists for (1.1) if the end states are close and satisfy the Rankine-Hugoniot condition. For such a travelling wave, we shall show that if the initial data are close to a travelling wave solution, the solutions to (1.1) will approach the travelling wave solution in sup norm as the rime goes to infinity, For the constitutive relations, we shall discuss two cases: convex and nonconvex. (C) 1996 Academic Press, Inc.

  • ON THE DECAY PROPERTY OF SOLUTIONS TO THE CAUCHY-PROBLEM OF THE SEMILINEAR WAVE-EQUATION WITH A DISSIPATIVE TERM

    S KAWASHIMA, M NAKAO, K ONO

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   47 ( 4 ) 617 - 653  1995.10  [Refereed]

  • EXISTENCE OF SHOCK PROFILES FOR VISCOELASTIC MATERIALS WITH MEMORY

    S KAWASHIMA, H HATTORI

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   26 ( 5 ) 1130 - 1142  1995.09  [Refereed]

     View Summary

    In this paper we discuss the necessary and sufficient conditions for the existence of smooth monotone shock profiles for viscoelastic materials with memory. We also discuss the uniqueness. We consider both convex and nonconvex constitutive relations. In the case of nonconvex constitutive relations, we include a degenerate case where the speed of the shock profile is equal to the speed of the equilibrium characteristics at one of the end states. This was not discussed in previous literature.

  • ASYMPTOTIC EQUIVALENCE OF A REACTION-DIFFUSION SYSTEM TO THE CORRESPONDING SYSTEM OF ORDINARY DIFFERENTIAL-EQUATIONS

    H HOSHINO, S KAWASHIMA

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   5 ( 6 ) 813 - 834  1995.09  [Refereed]

     View Summary

    Large time behavior of the solution to some simple reaction-diffusion system is studied. It is proved that the solution behaves like the solution to the corresponding system of ordinary differential equations as time goes to infinity. The proof is based on an energy method combined with the L(p)-L(q) estimate for the associated semigroup.

  • ON THE NEUMANN PROBLEM OF ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY WITH TIME-INDEPENDENT EXTERNAL FORCES

    S KAWASHIMA, Y SHIBATA

    CZECHOSLOVAK MATHEMATICAL JOURNAL   45 ( 1 ) 39 - 67  1995  [Refereed]

  • On solutions to utt |x|α Δu = f (u) (α>0)

    Y. Ebihara, S. Kawashima, H.A. Levine

    Funkcialaj Ekvacioj   38   539 - 544  1995

  • STABILITY OF SHOCK PROFILES IN VISCOELASTICITY WITH NONCONVEX CONSTITUTIVE RELATIONS

    S KAWASHIMA, A MATSUMURA

    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS   47 ( 12 ) 1547 - 1569  1994.12  [Refereed]

  • Asymptotic behavior of solutions to the Burgers equation with a nonlocal term

    K. Ito, S. Kawashima

    Nonlinear Analysis   23   1533 - 1569  1994  [Refereed]

  • THE DISCRETE BOLTZMANN-EQUATION WITH MULTIPLE COLLISIONS AND THE CORRESPONDING FLUID-DYNAMICAL EQUATIONS

    S KAWASHIMA

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   3 ( 5 ) 681 - 692  1993.10  [Refereed]

  • GLOBAL-SOLUTIONS TO THE EQUATION OF VISCOELASTICITY WITH FADING MEMORY

    S KAWASHIMA

    JOURNAL OF DIFFERENTIAL EQUATIONS   101 ( 2 ) 388 - 420  1993.02  [Refereed]

  • Self-similar solutions of a convection-diffusion equation

    S. Kawashima

    Nonlinear PDE-JAPAN Symposium 2 (K. Masuda, M. Mimura and T. Nishida, eds.)   12   123 - 136  1993

  • GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SMALL SOLUTIONS TO NONLINEAR VISCOELASTICITY

    S KAWASHIMA, Y SHIBATA

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   148 ( 1 ) 189 - 208  1992.08  [Refereed]

     View Summary

    The global existence of smooth solutions to the equations of nonlinear hyperbolic system of 2nd order with third order viscosity is shown for small and smooth initial data in a bounded domain of n-dimensional Euclidean space with smooth boundary. Dirichlet boundary condition is studied and the asymptotic behaviour of exponential decay type of solutions as t tending to infinity is described. Time periodic solutions are also studied. As an application of our main theorem, nonlinear viscoelasticity, strongly damped nonlinear wave equation and acoustic wave equation in viscous conducting fluid are treated.

  • Exponential stability of stationary solutions to the discrete Boltzmann equation in a bound ed domain

    S. Kawashima

    Math. Models Meth. Appl. Sci.   2   239 - 248  1992

  • Large-time behavior of solutions to the discrete Boltzmann equation in the half-space

    S. Kawashima

    Transport Theor. Stat. Phys.   21   451 - 463  1992

  • Existence and stability of stationary solutions to the discrete Boltzmann equation

    Shuichi Kawashima

    Japan Journal of Industrial and Applied Mathematics   8 ( 3 ) 389 - 429  1991.10

     View Summary

    The initial-boundary value problems and the corresponding stationary problems of the discrete Boltzmann equation are studied. It is shown that stationary solutions exist for any boundary data. These stationary solutions are unique in a neighborhood of a given constant Maxwellian. Furthermore, it is proved that if both initial and boundary data are close to a given constant Maxwellian, then unique solutions to the initial-boundary value problems exist globally in time and converge to the corresponding unique stationary solutions exponentially as time goes to infinity. The stability condition plays an essential role in proving the uniqueness and the time-asymptotic stability results. © 1991 JJIAM Publishing Committee.

    DOI

  • Asymptotic behavior of solutions to the discrete Boltzmann equation, Discrete Models of fluid Dynamics (A.S. Alves, ed.)

    S. Kawashima

    Series on Advances in Mathematics for Appli ed Sciences   2   35 - 44  1991  [Refereed]

  • On the Euler equation in discrete kinetic theory, Advances in Kinetic Theory and Continuum Mechanics (R. Gatignol and Soubbaramayer, eds.)

    S. Kawashima, N. Bellomo

    Springer-Verlag     73 - 80  1991

  • GLOBAL-SOLUTIONS TO THE INITIAL-BOUNDARY VALUE-PROBLEMS FOR THE DISCRETE BOLTZMANN-EQUATION

    S KAWASHIMA

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   17 ( 6 ) 577 - 597  1991  [Refereed]

  • The Boltzmann equation and thirteen moments

    Shuichi Kawashima

    Japan Journal of Applied Mathematics   7 ( 2 ) 301 - 320  1990.06

     View Summary

    The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments. © 1990 JJAM Publishing Committee.

    DOI

  • THE DISCRETE BOLTZMANN-EQUATION WITH MULTIPLE COLLISIONS - GLOBAL EXISTENCE AND STABILITY FOR THE INITIAL-VALUE PROBLEM

    N BELLOMO, S KAWASHIMA

    JOURNAL OF MATHEMATICAL PHYSICS   31 ( 1 ) 245 - 253  1990.01  [Refereed]

  • The Navier-Stokes equation associated with the discrete Boltzmann equation

    S. Kawashima, Y. Shizuta

    Recent Topics in Nonlinear PDE IV (M. Mimura, T. Nishida, eds.), Lecture Notes in Num. Appl. Anal.   10   15 - 30  1989  [Refereed]

  • A new approach to the Boltzmann equation, Discrete Kinetic Theory, Lattice Gas Dynamics, Foundation of Hydrodynamics (R. Monaco, ed.)

    S. Kawashima

    World Scientic     192 - 205  1989

  • Initial-value problem in discrete kinetic theory, Rarefied Gas Dynamics: Theoretical, Computational Techniques (E.P. Muntz, D.P. Weaver, D.H. Campbell, eds.)

    S. Kawashima, H. Cabannes

    Progress in Astronautics and Aeronautics   118   148 - 154  1989

  • ON THE NORMAL-FORM OF THE SYMMETRIC HYPERBOLIC-PARABOLIC SYSTEMS ASSOCIATED WITH THE CONSERVATION-LAWS

    S KAWASHIMA, Y SHIZUTA

    TOHOKU MATHEMATICAL JOURNAL   40 ( 3 ) 449 - 464  1988.09  [Refereed]

  • Le problème aux valeurs initiales en théorie cinétique discrète

    H. Cabannes, S. Kawashima

    C. R. Acad. Sci. Paris   307   507 - 511  1988

  • The Navier-Stokes equation in the discrete kinetic theory

    S. Kawashima, Y. Shizuta

    J. Mècan. thèor. appl.   7   597 - 621  1988  [Refereed]

  • Initial-boundary value problem for the discrete Boltzmann equation

    S. Kawashima

    Journèes Èquations aux Dèrivèes Partielles, Centre de Mathèmatiques    1988

  • Weak solutions with a shock for a model system of the radiating gas

    S. Kawashima, S. Nishibata

    Science Bulletin of Josai Univ.   5   119 - 130  1988

  • MIXED PROBLEMS FOR QUASI-LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS

    S KAWASHIMA, T YANAGISAWA, Y SHIZUTA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   63 ( 7 ) 243 - 246  1987.09  [Refereed]

  • THE REGULAR DISCRETE MODELS OF THE BOLTZMANN-EQUATION

    Y SHIZUTA, S KAWASHIMA

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   27 ( 1 ) 131 - 140  1987.02  [Refereed]

  • Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications

    S. Kawashima

    Proc. Roy. Soc.   106A   169 - 194  1987  [Refereed]

  • LARGE-TIME BEHAVIOR OF SOLUTIONS OF THE DISCRETE BOLTZMANN-EQUATION

    S KAWASHIMA

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   109 ( 4 ) 563 - 589  1987  [Refereed]

  • Asymptotic stability of Maxwellians of the discrete Boltzmann equation

    S. Kawashima

    Transport Theor. Stat. Phys.   16   781 - 793  1987

  • The Boltzmann equation and thirteen moments

    S. Kawashima

    Recent Topics in Nonlinear PDE III (K. Masuda, T. Suzuki, eds.) Lecture Notes in Num. Appl. Anal.   9   157 - 172  1987

  • On compactly support ed solutions of the compressible Euler equation

    T. Makino, S. Ukai, S. Kawashima

    Recent Topics in Nonlinear PDE III (K. Masuda, T. Suzuki, eds.) Lecture Notes in Num. Appl. Anal.   9   173 - 183  1987

  • THE 102-VELOCITY MODEL AND THE RELATED DISCRETE MODELS OF THE BOLTZMANN-EQUATION

    Y SHIZUTA, M MAEJI, A WATANABE, S KAWASHIMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   62 ( 10 ) 367 - 370  1986.12  [Refereed]

  • LARGE-TIME BEHAVIOR OF SOLUTIONS FOR HYPERBOLIC-PARABOLIC SYSTEMS OF CONSERVATION-LAWS

    S KAWASHIMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   62 ( 8 ) 285 - 287  1986.10  [Refereed]

  • ASYMPTOTIC-BEHAVIOR OF SOLUTIONS FOR THE EQUATIONS OF A VISCOUS HEAT-CONDUCTIVE GAS

    S KAWASHIMA, A MATSUMURA, K NISHIHARA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   62 ( 7 ) 249 - 252  1986.09  [Refereed]

  • REGULARITY OF THE 90-VELOCITY MODEL OF THE BOLTZMANN-EQUATION

    Y SHIZUTA, M MAEJI, A WATANABE, S KAWASHIMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   62 ( 5 ) 171 - 173  1986.05  [Refereed]

  • Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid

    S. Kawashima, Y. Shizuta

    Tsukuba J. Math.   10   131 - 149  1986

  • Magnetohydrodynamic approximation of the complete equations for an electromagneticfluid II

    S. Kawashima, Y. Shizuta

    Proc. Japan Acad.   62   181 - 184  1986

  • On Cabannes' 32-velocity models of the Boltzmann equation

    S. Kawashima, A. Watanabe, M. Maeji, Y. Shizuta

    Publ. RIMS Kyoto Univ.   22   583 - 607  1986  [Refereed]

  • Sur la solution ä support compact de l'equation d'Euler compressible

    T. Makino, S. Ukai, S. Kawashima

    Japan J. Appl. Math.   3   249 - 257  1986

  • Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation

    Yasushi Shizuta, Shuichi Kawashima

    Hokkaido Mathematical Journal   14 ( 2 ) 249 - 275  1985

    DOI

  • ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS OF SYSTEMS FOR ONE-DIMENSIONAL GAS MOTION

    S KAWASHIMA, A MATSUMURA

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   101 ( 1 ) 97 - 127  1985  [Refereed]

  • THE REGULARITY OF DISCRETE MODELS OF THE BOLTZMANN-EQUATION

    Y SHIZUTA, S KAWASHIMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   61 ( 8 ) 252 - 254  1985  [Refereed]

  • On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics

    Tomio Umeda, Shuichi Kawashima, Yasushi Shizuta

    Japan Journal of Applied Mathematics   1 ( 2 ) 435 - 457  1984.12

     View Summary

    The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)-3/4 in L2(R3) holds for solutions of the above equations, provided that the initial data are in L2(R3)∩L1(R3). Since the systems of equations are not rotationally invariant, the perturbation theory for one parameter family of matrices is not useful enough to derive the above result. Therefore, by exploiting an energy method, we show that the decay estimate holds for the solutions of a general class of equations of symmetric hyperbolic-parabolic type, which contains the linearized equations in both electro-magneto-fluid dynamics and magnetohydrodynamics. © 1984 JJAM Publishing Committee.

    DOI

  • Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics

    Shuichi Kawashima

    Japan Journal of Applied Mathematics   1 ( 1 ) 207 - 222  1984.09

     View Summary

    The equations of an electrically conducting compressible fluid in electro-magneto-fluid dynamics are studied. It is proved that in a certain case of two-dimensional flow, the equations of the fluid become a symmetric hyperbolic-parabolic system in both of the viscous and non-viscous cases. Therefore, the initial value problem is well posed in the Sobolev spaces at least for short time interval. Furthermore, in the viscous case, the solution exists globally in time and tends to the constant state as time goes to infinity, provided the initial data are closed to the constant state. The proof is based on a technical energy method, which makes use of a quadratic function associated with the total energy of the fluid. © 1984 JJAM Publishing Committee.

    DOI

  • ON THE EQUATIONS OF ONE-DIMENSIONAL MOTION OF COMPRESSIBLE VISCOUS FLUIDS

    M OKADA, S KAWASHIMA

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   23 ( 1 ) 55 - 71  1983  [Refereed]

  • Global existence and stability of solutions for discrete velocity models of the Boltzmann equation

    S. Kawashima

    Recent Topics in Nonlinear PDE (M. Mimura, T. Nishida, eds.), Lecture Notes in Num. Appl. Anal.   6   59 - 85  1983

  • SMOOTH GLOBAL-SOLUTIONS FOR THE ONE-DIMENSIONAL EQUATIONS IN MAGNETOHYDRODYNAMICS

    S KAWASHIMA, M OKADA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   58 ( 9 ) 384 - 387  1982  [Refereed]

  • GLOBAL SOLUTION OF THE INITIAL VALUE-PROBLEM FOR A DISCRETE VELOCITY MODEL OF THE BOLTZMANN-EQUATION

    S KAWASHIMA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   57 ( 1 ) 19 - 24  1981  [Refereed]

  • The asymptotic equivalence of the Broadwell model equation and its Navier-Stokes model equation

    Shuichi Kawashima

    Japanese Journal of Mathematics   7 ( 1 ) 1 - 43  1981

    DOI

  • GLOBAL-SOLUTIONS TO THE INITIAL-VALUE PROBLEM FOR THE EQUATIONS OF ONE-DIMENSIONAL MOTION OF VISCOUS POLYTROPIC GASES

    S KAWASHIMA, T NISHIDA

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   21 ( 4 ) 825 - 837  1981  [Refereed]

  • On the fluiddynamical approximation to the Boltzmann equation at the level of the NavierStokes equation

    S. Kawashima, A. Matsumura, T. Nishida

    Commun.Math. Phys.   70   97 - 124  1979

  • Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws

    K. Nakamura, T. Nakamura, S. Kawashima

    preprint  

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Awards

  • 2018年度日本数学会解析学賞

    2018.09   一般社団法人日本数学会   消散構造を持つ非線形偏微分方程式系の安定性解析

    Winner: 川島秀一

Research Projects

  • New developments in mathematical analysis of spatio-temporal nonuniform dynamics in quasilinear hyperbolic-parabolic conservation laws

    Project Year :

    2020.04
    -
    2024.03
     

  • Creation of advanced method in mathematical analysis on nonlinear mathematical models of critical type

    Project Year :

    2019.06
    -
    2024.03
     

  • Unravel higher order critical structures to solutions of nonlinear dispersive and dissipative partial differential equations

    Project Year :

    2019.04
    -
    2024.03
     

  • Entropy dissipative structure and mathematical analysis for complex fluids

    Project Year :

    2018.04
    -
    2022.03
     

  • 複雑流体のエントロピー消散構造と数理解析

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    2018
    -
    2021
     

  • Unravel higher order critical structures to solutions of nonlinear dispersive and dissipative partial differential equations

    Project Year :

    2019.04
    -
    2020.03
     

  • 圧縮流体方程式の時空非一様ダイナミクスの数学解析

    Project Year :

    2016.04
    -
    2020.03
     

     View Summary

    1. 2次元無限層状領域における圧縮性Navier-Stokes方程式の時空間周期解の周りの線形化発展作用素のスペクトル構造を空間変数に関するBloch変換と時間変数に関するFloquet解析を用いて調べたが,その解析にもとづいて今年度はさらに非線形相互作用を解析し,非線形問題の解の漸近挙動を調べた.結果を論文にまとめているところである.2. 非圧縮Navier-Stokes方程式とその特異摂動系である人工圧縮方程式系について,両方程式系の定常解のまわりの線形化作用素のスペクトルの関係における境界層の影響を調べた.人工圧縮方程式系は非圧縮Navier-Stokes方程式の連続の方程式に小さいパラメータ(マッハ数)を乗じた圧力の時間微分を加えて得られる半線形の双曲-放物型方程式系であり,圧縮性Navier-Stokes方程式と同じく非圧縮Navier-Stokes方程式をマッハ数ゼロの極限としてもつ.前年度までの研究によって,マッハ数が小さければ,定常分岐解の分岐安定性構造は,人工圧縮系と非圧縮系とでは同一になることがわかっていたが,今年度は人工圧縮方程式系のHopf分岐の特異極限問題を考察し,非圧縮性Navier-Stokes方程式においてHopf分岐が起こるとき,マッハ数が小さければ人工圧縮方程式系でもHopf分岐が起こることを示した.現時点では,マッハ数に関する一様評価が成立するかどうかは一般にはわからない状況である.このことは定常分岐問題の結果とは異なる.しかしながら,Hopf分岐の場合でも,静止状態からHopf分岐が起こる場合はマッハ数に関する一様評価が得られることを示し,この評価により,マッハ数が小さければ,Hopf分岐時間周期解の分岐・安定性構造が非圧縮系と人工圧縮系とで同一のものとなることを示した.例として,塩分濃度を考慮に入れた熱対流問題があげられる.この結果を論文にまとめているところであり,一般の場合は今後の課題として残った.無限層状領域における圧縮性Navier-Stokes方程式の時空間周期解のまわりの線形化発展作用素のスペクトル構造の空間変数に関するBloch変換および時間変数に関するFloque解析にもとづいて,非線形問題の解の漸近挙動の詳細を得ることができた.人工圧縮方程式系の時間周期解のまわりの線形化発展作用素に対するFloquet解析を実行するために,マッハ数の重み付きのノルムを導入したエネルギー法を完成させ,ある状況下ではマッハ数に関する一様評価をともなう形でFloquet解析を行うことができた.このことにより,圧縮性Navier-Stokes方程式の時空間周期解のまわりでの時間発展問題に対するマッハ数ゼロの特異極限問題の解析への道が開けてきた.前年度に引き続き,人工圧縮系の定常解まわりの線形化作用素のスペクトルに関して,虚部がマッハ数の逆数のオーダーの部分のスペクトルの形式的漸近展開に数学的証明を与え,非線形安定性を考察する.さらに,その解析を圧縮性テイラー渦のまわりの解のダイナミクスの解析へと拡張する.人工圧縮系のHopf分岐に関して一般の定常解から時間周期解が分岐する場合に,マッハ数に関する一様評価の導出を行い,圧縮性Navier-Stokes方程式のHopf分岐問題への解析へとつなげる

  • Elucidations on unexplored regions of problems related to the criticality of nonlinear dissipative and dispersive structures in mathematical models

    Project Year :

    2013.05
    -
    2018.03
     

     View Summary

    We extract a dispersive and dissipative effect from the typical example in the nonlinear dispersive equations such as the nonlinear Schroedinger equation and nonlinear dissipative equations such as the Navier-Stokes system or the drift diffusion system and research the critical problems that arose from a balanced situation between the stabilize effects from dispersive and dissipative and the instability caused from nonlinear interaction. In particular, we establish the maximal regularity for the nonlinear dissipative system and applied for the critical problems and singular limit problems in Keller-Segel system or ill-posedness problem of mathematical fluid mechanics

  • 非線形発展方程式の未踏臨界構造の解明

    Project Year :

    2013.04
    -
    2018.03
     

     View Summary

    研究代表者の小川は研究協力者の岩渕 司と共同で, 2乗のべき型非線形項を持つ非線形シュレディンガー方程式の適切性と非適切性の臨界を研究し, 空間1次元においては非斉次Sobolev空間のもつ非斉次構造が, 不変スケールから予想される臨界スケールに至ることを阻害することを示し, さらに臨界性を実補間空間であるベソフ空間で分類した場合の臨界補間指数を同定した. また2次元に対しては予想される臨界スケールに至ることを示した. 4次元以上においては堤誉志雄による最良の結果が知られており, 2次の非線型性に対して残る問題は3次元のみとなった. また同様の事実は非線形熱方程式に対しても成立することを述べた. これらの結果は解の形式的な漸近展開を, モデュレーション空間において正当化し, 解の2次近似が臨界空間よりも広いクラスで解の不安定性を引き起こすことに起因する. 漸近展開を正当化することにより, 従来あった背理法による議論を経由せずに証明が可能となる. 一方, 半導体モデルに現れる, 移流拡散方程式には双極性のモデルと単極性モデルが存在する. 双方の初期値問題に対しても同様な臨界適切性を研究し, 双極性のモデルは単極モデルよりも適切な函数空間のクラスが狭いことを, 非線形干渉の対称性に着目して示した. また副産物として, 2次元渦度のNavier-Stokes方程式の可解性について既存の結果が双極型移流拡散方程式の非線形項と類似であるにもかかわらず, 単極型と同等の函数空間まで適切性が示されることについて, 非圧縮条件が非線形構造に対して対称性を与えることに起因することを突き止めた.25年度が最終年度であるため、記入しない。25年度が最終年度であるため、記入しない

  • Analysis of stablity and bifurcation for compressible fluid equations

    Project Year :

    2012.04
    -
    2016.03
     

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    To establish mathematical theory for bifurcation and stability in the compressible Navier-Stokes equation, we studied the stability of stationary and time-periodic parallel flows. We proved that the asymptotic behavior of parallel flow is described by a linear heat equation when the space dimension n is greater than or equal to 3, and by a one-dimensional viscous Burgers equation when n=2. In the case of the Poiseuille flow, we derived a sufficient condition for the instability in terms of the Reynolds and Mach numbers. Furhtermore, we proved the bifurcation of a familiy of space-time-peirodic traveling waves when the Poiseuille flow is getting unstable. As a first step of the stability analysis of space-periodic patterns, we investigate the stablity of the motionless state on periodic infinte layer, and derived the asymptotic leading part of the perturbation by using the Bloch transformation

  • Stability analysis for nonlinear partial differential equations

    Project Year :

    2010.04
    -
    2015.03
     

     View Summary

    We studied systems of nonlinear partial differential equations in the fields of gas dynamics, elasto-dynamics and plasma physics. We investigated the dissipative structure and decay property of the systems and proved the asymptotic stability of various nonlinear phenomena of vibration and wave propagation. Also we developed a general theory on nonlinear stability analysis for hyperbolic systems of conservation equations with relaxation and observed that the time-weighted energy method, semigroup approach and the technique of harmonic analysis are useful in the stability analysis

  • 非線形偏微分方程式に対する安定性解析

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    2010
    -
    2014
     

  • Research for Critical Asymptotic Structure of Nonlinear Evolution Equations

    Project Year :

    2008.04
    -
    2013.03
     

     View Summary

    The main reseacher T. Ogawa researched several nonlinear partial differential equations with critical structure and find various criticality in each problems. He studied the following topics with colabolators. Two dimensional drift-diffusion system in the critical Besov spaces and established maximal regularity for the heat equation in non-reflexivie Banach spaces. Higher order expansion of the solution for the drift-diffusion system in higher space dimensions, the global existence for the nonlinear damped wave system, the critical Sobolev inequality with logarithmic type and generalization to abstract Besov spaces, WKB approximation for nonlinear Schrodinger equations with Poisson equations, the scaling critical solvabilityfor quadratic nonlinear Schrodinger equation and critical well-posedeness in lower space dimensions

  • Characterization of dissipative structure for partial differential equations and application to the nonlinear stability analysis

    Project Year :

    2006
    -
    2009
     

     View Summary

    We studied nonlinear partial differential equations in the field of gas dynamics, fluid dynamics and elasto-dynamics. We investigated the dissipative properties of the systems and proved the asymptotic stability of various nonlinear phenomena

  • 偏微分方程式系における消散構造の特徴付けと非線形安定性解析への応用

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    2006
    -
    2009
     

  • 気体の方程式系の解の漸近挙動と非線形波の安定性に関する研究

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    2002
    -
    2005
     

  • 輻射気体の方程式系の基本解とその応用に関する研究

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    1999
    -
    2001
     

  • 準線形双曲・楕円型連立方程式系の初期値問題に関する研究

    独立行政法人日本学術振興会  科学研究費助成事業

    Project Year :

    1995
    -
    1997
     

  • Studies on singular perturbation problems in nonlinear mechanics

     View Summary

    (1) New phenomena on the Navier-Stokes equations were found. Among others, solutions having interior layers and those solutions having k-10 spectra are remarkable. (2) Bifurcation phenomena in surface waves were clarified. In particular, an accurate numerical method was developed for singular solitary waves. (3) dynamical systems viewpoints on the shell model of turbulence proposed by Ohkitani and Yamada were enhanced. (4) applications to reaction-diffusion systems, (5) vortex formation in the 2-dimensional decaying turbulence by Y. Kimura. (6) asymptotic behavior of shock wave solutions was clarified by Kawashima and Matsumura.Okamoto, with the aid by Kim Sunchul, analyzed the bifurcating solutions arising in the rhombic periodic flows. It was demonstrated, by an elaborate numerical computations, that some solutions have k-10 spectra as the Reynolds number tends to infinity. Okamoto and A. Craik considered a three-dimensional dynamical system arising in fluid mechanics. Two different solutions, one with 90-degree bending and one without bending, were found and the mechanism of them was theoretically explained.Y. Kimura, with J. Herring, successfully explained theoretical background of vortex structures arising in rotating fluid. S. Kawashima proved the well-posedness of radiating gases.T. Ikeda considered models for combustion synthesis. With numerical experiments he demonstrated that the solutions of the model can reproduce the results of the laboratory experiments.H. Ikeda and H. Okamoto considered a special solution of the Navier-Stokes equations called Oseen flows. Some interior layers was rigorously proved. H. Ikeda also proved that a Hopf bifurcation occurs in the traveling wave solutions of a certain bi-stable system of reaction diffusion.H. Fujita proved the existence of the solutions of the Navier-Stokes equations when they are subjected to a leak boundary condition. He also derived a new convergence rate of the domain-decomposition method.M. Yamada and K. Ohkitani discovered, by a numerical experiments, a time-periodic solution, which simulate the turbulent motions of real flows

  • Study on the fundamental solutions to the equations of radiating gases and its applications

     View Summary

    We study the stability of nonlinear waves for hyperbolic-elliptic coupled systems in radiation hydrodynamics and related equations.1. By using the Fourier transform, we give a representation formula for the fundamental solutions to the linearized systems of hyperbolic-elliptic coupled systems and verify that the principal part of the fundamental solutions is given explicitly in terms of the heat kernel. Also, we obtain the sharp pointwise estimates for the error terms.2. We obtain the pointwise decay estimate of solutions to the hyperbolic-elliptic coupled systems by using the representation formula for the fundamental solution and the corresponding estimates. Furthermore, we prove that the solution is asymptotic to the superposition of diffusion waves which propagate with the corresponding characteristic speeds.3. We discuss a singular limit of the hyperbolic-elliptic coupled systems. We prove that at this limit, the solution of the hyperbolic-elliptic coupled system converges to that of the corresponding hyperbolic-parabolic coupled system.4. We show the existence of stationary solutions to the discrete Boltzmann equation in the half space. It is proved that the stationary solution approaches the far field exponentially and is asymptotically stable for large time.5. We study the asymptotic behavior of nonlinear waves for the isentropic Navier-Stokes equation in the half space. For the out-flow problem, we prove the asymptotic stability of nonlinear waves such as (1)stationary wave, (2)rarefaction wave, and (3)superposition of stationary wave and rarefaction wave

  • Asymptotic Analysis for Singularities of Solutions to Nonlinear Partial Differential Equations

     View Summary

    The head investigator, T. Ogawa researched with one of the research collaborator K. Kato that the solution of the semi-linear dispersive equation has a very strong type of the smoothing effect called "analytic smoothing effect" under a certain condition for the initial data. This result says that from an initial data having a strong single singularity such as the Dirac delta measure, the solution for the Korteweb-de Vries equation is immediately going to smooth up to real analytic in both space and time variable. Similar effect can be shown for the solutions of the nonlinear Schroedinger equations and Benjamin-Ono equations.Also with collaborators H. Kozono and Y. Taniuchi, Ogawa showed that the uniqueness and regularity criterion to the incompressible Navier-Stokes equations and Euler equations. Besides, it is also given that the solution to the harmonic heat flow is presented in terms of the Besov space. Those result is obtained by improving the critical type of the Sobolev inequalities in the Besov space. On the same time, the sharper version of the Beale-Kato-Majda type inequality involving the logarithmic term was obtained by using the Lizorkin-Triebel interpolation spaces.For the equation appeared in the semiconductor devise simulation, the head organizer Ogawa showed with M. Kurokiba that the solution has a global strong solution in a weighted L-2 space and showed some conservation laws as well as the regularity. Besides, under a special threshold condition, the solution develops a singularity within a finite time.It is also shown that the threshold is sharp for a positive solutions.Co-researcher S. Kawashima investigated the asymptotic behavior of the solutions to a general elliptic-hyperbolic system including the equation for the radiation gas. The asymptotic behavior can be characterized by the linearized part of the system and it is presented by the usual heat kernel.Co-researcher Y.Kagei researched with co-researcher T.Kobayashi about the asymptotic behavior of the solutions to the incompressible Navier-Stokes in the three dimensional half space. They studied on the stability of the constant density steady state for the equation and the showed the best possible decay order of the perturbed solution in the sense of L-2.Co-researcher K. Ito studied about the intermediate surface diffusion equation and showed that the solution has the self interaction when the diffusion coefficients are going to very large.Co-researcher N. Kita with T. Wada collaborates on the problem of the asymptotic expansion on the solution of the nonlinear Schroedinger equation when the time parameter goes infinity. They identified the second term of the asymptotic profile of the scattering solution when the nonlinearity has the threshold exponent of the long range interaction

  • Dynamics of solutions near space-periodic bifurcating steady solutions of thermal convection equations

     View Summary

    Y.Kagei showed that some stationary solutions of the Obebeck-Boussinesq equation is unconditionally stable even when they are at criticality of the linearized stability. Kagei then derived a model equation of thermal convection in which the effect of viscous dissipative heating is taken into account. It was shown that the threshold of the onest of convection for this model equation is larger than that for the usual Oberbeck-Boussinesq equation and various space-periodic stationary solutions bifurcate at the threshold transcritically. Kagei also studied the Cauchy problem for the Vlasov-Poisson-Fokker-Planck equation and constructed invariant manifolds in some weighted Sobolev spaces. As a result, long-time asymptotics of small solutions were derived. S.Kawashima studied a singular limit problem for a general hyperbolic-elliptic system and proved that in the singular limit the solution of the hyperbolic-elliptic system converges to the solution of the corresponding hyperbolic-parabolic system. Kawashima also studied initial boundary value problems for discrete Boltzmann equations in the half-space and showed the existence of stationary solutions under several boundary conditions and their asymptotic stability. T.Ogawa showed that for a class of semilinear dispersive equations, solutions with initial values having one singular point like the Dirac delta function become real analytic in space and time variables except at the initial time. Ogawa also studied blow-up problem for the three dimensional Euler equation and gave a sufficient condition for blow-up in terms of some semi-norm of a generalized Besov space. T.Iguchi studied bifurcation problem of stationary surface waves and classified possible bifurcation patterns

  • Exterior problem for nonlinear wave equations

     View Summary

    The main purpose of this research is concerned with the exterior problem for the quasi-linear wave equations. For this problem we have been successful in proving the global existence of smooth solutions under the effect of localized dissipation. We have achieved the results through two ways; one is based on the local energy decay and L^p estimates of solutions for linear equation, and the other one is the method to utilize total energy decay for the llinearized equation. Both ways are intended to make the effects of dissipation as weaker as possible, but, we have made no geometrical conditions on the shape of the boundary.Concerning another problem on the energy decay for the equation with nonlinear dissipations we introduced anew concept ‘Half linear' and has been successful in deriving very delicate decay estimates of energy and applied them to the existence of global solutions for the equations with a nonlinear source term.As related problems we have considered the existence and stability of periodic solutions for the nonlinear wave equations in bounded domains with some nonlinear localized dissipations. Further, we have considered the Kirchhoff type nonlinear wave equations in exterior domains. Under a nonlinear dissipations we have proved various results on global solutions. For the wave equation in exterior domains with a Neumann type boundary dissipation we have derived a new energy decay estimate.Investigator Kawashima has derived many interesting results concerning Boltzman equations and hyperbolic conservation equations. Investigator Shibata has derived by the method of spectral analysis, many interesting results concerning the exterior problem for the compressive Navier-Stokes equations. Investigator Ogawa has proved precise estimates of solutions concerning behaviors and regularities of solutions for the nonlinear wave equations, nonlinear Shroadinger equations and some harmonic evolution equation

  • 粘性流体と分散型非線形方程式研究に関する日韓国際共同研究

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    研究実績は以下のとおり.研究代表者の小川は研究分担者の加藤と共に,非線型分散系の方程式についてBenjamin-Ono方程式の初期値問題の解がその初期値に一点のみSobolev空間H^S(s>3/2)程度の特異点を持つ場合に、対応する弱解が時間が立てば、時間、空間両方向につき実解析的となるsmoothing effectを持つことを示した。その過程で、無限連立のBenjamin-Ono型連立系の時間局所適切性を証明した。またKdV方程式とBenjamin-Ono方程式の中間的な効果を表すBenjaminのoriginal方程式に関して、その初期値問題が負の指数をも許すSobolev空間H^s(R)(s>-3/4)で時間局所的に適切となることを示した。さらに、谷内と共同で臨界型の対数形Sobolevの不等式(Brezis-Gallouetの不等式)を斉次,非斉次Besov空間に拡張した。またそれを用いて非圧縮性Navier-Stokes方程式、Euler方程式、及び球面上への調和写像流の解の正則延長のための十分条件をこれまでに知られているSerrin型の条件よりも拡張した。これらの結果を元に、韓国ソウル国立大学数学科のD-H. Chae氏との共同研究をめざす、研究交流を行った分担者の川島は一般の双曲・楕円型連立系のある種の特異極限を論じた。この特異極限で双曲・楕円型連立系の解が対応する双曲・放物型連立系の解に収束することを、その収束の速さも込めて証明した。また、輻射気体の方程式系ではこの特異極限は、Boltzmann数とBouguer数の積を一定にしたままBoltzmann数を零に近づける極限に対応していることを明らかにした。分担者の隠居はVlasov-Poisson-Fokker-Planck方程式(VPFP方程式)の初期値問題に対して,重み付きソボレフ空間において不変多様体を構成し、解の時間無限大での漸近形を導出した

  • Asymptotic behavior of solutions and stability of nonlinear waves for equations of gas motion

     View Summary

    We studied asymptotic behavior of solutions and stability of nonlinear waves for equations of gas motion with dissipative structure.1.We developed the energy method in the Sobolev space W^{1,p} for n-dimensional scalar viscous conservation law and derived the optimal decay estimates in W^{1,p}. The method was also applied to the stability problem for rarefaction waves and stationary waves.2.We introduced the notion of entropy for n-dimensional hyperbolic conservation laws with relaxation and developed the Chapman-Enskog theory. Moreover, we proved the global existence and optimal decay of solutions in a L^2 type Sobolev space.3.For the compressible Navier-Stokes equation in the n-dimensional half space, we proved the asymptotic stability of planar stationary waves. To develop the theory in the Sobolev space of order [n/2]+1, we need additional considerations for local existence results.4.For the dissipative Timoshenko system, we derived qualitative decay estimates of solutions by applying the energy method in Fourier space. We found that the dissipative structure is so weak in high frequency region and it causes the regularity loss in the decay estimates.5.For dissipative wave equation with a nonlinear convection term, we proved the global existence and optimal decay of solutions in L^p. Moreover, we showed that the solution approaches the nonlinear diffusion waves given in terms of the self similar solutions of the Burgers equation. Derivation of detailed pointwise estimates of the fundamental solutions is crucial in the proof

  • Mathematical analysis of thermal convection equations

     View Summary

    Y.Kagei and T.Kobayashi investigated the stability of the motionless equilibrium with constant density of the compressible Navier-Stokes equation on the half space and gave a solution formula for the linearized problem to derive decay estimates for solutions to the linearized problem. Combining these results with the energy method, they obtained decay estimates for perturbations. The results also indicate that there may be some nonlinear interaction phenomena not appearing in the Cauchy problem. Kagei studied a nonhomogeneous Navier-Stokes equations for thermal convection motions. He showed the existence of global weak solutions and investigated the Oberbeck-Boussinesq limit of the equation under consideration. Kobayashi investigated local interface regularity of solutions of the Maxwell equation, Stokes equation and Navier-Stokes equation. S. Kawashima proved that the solution of a general hyperbolic-elliptic system are approximated in large times by the ones of the corresponding hyperbolic-parabolic system. Kawashima also established the $W^{1.p}$-energy method for multi-dimensional viscous conservation laws and obtained the sharp $W^{1.p}$ decay estimates. Kawashima gave a notion of an entropy for hyperbolic systems of balance laws, which enables to understand the dissipative structure of the systems. T.Ogawa extended the logarithmic Sobolev inequalities to homogenous and inhornogeneous Bosev spaces. Using these inequalities he improved the Serrin-type condition for regularity of solutions to the incompressible Navier-Stokes equation, Euler equation and Harmonic flows. Ogawa also proved the finite-time blow up of solutions to the drift-diffusion equations. T.Iguchi studied the bifurcation problem of water waves and classified the bifurcation patters in terms of the Fourier coefficients which represent the bottom of the domain. Iguchi also investigated conservation laws with a general flux. He introduced a notion of "piecewise genuinely nonlinear" and constructed the entropy solutions for the small initial values

  • Reseach for the singularities and regularity of solutions to crtical nonlinear partial differential equations

     View Summary

    The main researcher, Prof.Ogawa obtained the following results. He researched for the Sobolev type inequality of the critical type, especially for the real interpolation spaces such as Besov and Triebel-Lirzorkin spaces and generalized it for the abstract Besov and Lorentz space. Those inqualities involving the logarithmic interpolation order can be applied for the regularity and uniqueness criterion of the seimilinear partial differential equation. In a series of collaboration with the research colabolators, he shows that the reguarlity and uniquness criterion for the weak solution of the 3 dimensional Navier-Stokes equations and break down condition for the Euer equation. In a similar method, he also showed the regularity criterion for the smooth solution of the 2 dimensional harmonic heat flow into a sphere. In particular, for the weak solution of the harmonic heat flow, the similar regularity criterion is also holds. The result is obtained by establishing the "monotonicity formula" for the mean oscillation of the energy density of the solutions.He also consider the asymptotic behavior of the solution for the semi-lineear parabolic equation of the non-local type. Those system appeared in a various Physical scaling such as semi-conductor simulation model, Chemotaxis model and the birth of star in Astronomy. The system is involving Poisson equation as the field generated by the dencity of the charge or mucous ameba and the non-local effect is essential for the analysis of the solution. He particulariy investigated to the critical situation, 2-dimensional case, and showed that there exists a time local solution in the critical Hardy space, time global solution upto the threshold initial density and finite time blow-up for the system of forcusing drift-diffusion case. Besides, the asymootitic behavior of the solution for small data is characterized by the heat kernel. Moreover if the field equation is purterbed in a certain nonlinear way, then there exist two solutions for the same initial data in a radially symmetric case.He also studied for the asymptotic behavior of the solution for the semi-linear damped wave equation in whole and half spaces and exterior domains and show the small solution is going to be decomposed into the solutions of the linear heat equation, some combination of linear wave equation with nonlinear effect. This was shown for 1 and 3 dimensional cases before, however the mothod there could not be applicable for the 2dimensional case

  • Asymptotic behaivours of solutions for nonlinear wave equations

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    The main object of this project is to study the asymptotic behaviours of solutions of nonlinear wave equations through the investigation of global attractors. As related problems we also intended to investigate the energy decay problem for the wave equations and global attractors for nonlinear parabolic equations.First we considered the problem for the equations in bounded domains and established new results concerning the existence, sire and some absorbing properties of global attractors.Secondly, we considered the exterior problem fix Klein-Gordon type nonlinear wave equations and established a parallel results to the problem in bounded domains. In exterior domains the Sobolev spaces are not embedded I compactly into $1,^p$ spaces. This difficulty was overcome by the discover y that the local energy of solutions are controlled as small as we can near infinity when time also goes to infinity.In a joint work with Professor Y. Zhijiag from China we proved the existence and some exponential type absorbing of global attractors for some quasi-linear wave equations. This result generalize a known one for one space dimension to general dimensions.As related problems we give several results on global attractors for degenerate type quasi-linear parabolic equations which include estimates on smoothing effects. These are joint works with Prof C. Chen from China and Dr NT, Aris from Indonesia

  • Asymptotic analysis of systems of nonlinear partial differential equations describing motions of viscous fluids

     View Summary

    We studied the asymptotic behavior of solutions of the compressible Navier-Stokes equation which describes motion of viscous fluids. We analyzed the stability properties of stationary solutions such as the motionless state and parallel flows in detail. It was proved that these stationary solutions are asymptotically stable if they are small enough in some sense. Furthermore, it was shown that the disturbances behave like solutions of convective heat equations in large time

  • Stability and nonlinear structure for the nonlinear partial differential equations of gas dynamics.

     View Summary

    I analyzed the asymptotic stability of the nonlinear waves for some equations. Especially I focused on the nonlinearity which appears in the equation which describes a physical phenomenon. And I succeeded the construction of a certain kind of generalities.Furthermore, I considered some physical models and got the new dissipative structure of the equations

▼display all

Presentations

  • Dissipative structure for a model system of complex fluids

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 KMMビル) 

    Presentation date: 2018.11

  • Mathematical analysis for a model system of viscoelastic fluids

    川島秀一

    非線形解析セミナー  (慶応大学日吉キャンパス) 

    Presentation date: 2018.11

  • 双曲型平衡則系に対する数学解析

    川島秀一

    早稲田大学数学・応用数理談話会  (早稲田大学) 

    Presentation date: 2018.10

  • Mathematical analysis for a model system of complex fluids

    川島秀一

    RIMS共同研究(公開型)「非線形発展方程式を基盤とする現象解析に向けた数学理論の展開」  (京都大学数理解析研究所) 

    Presentation date: 2018.10

  • A model system of complex fluids and hyperbolic balance laws

    川島秀一

    非線形解析セミナー  (東京工業大学大岡山キャンパス) 

    Presentation date: 2018.07

  • A model system of viscoelastic fluids and related problems

    川島秀一

    信州大学偏微分方程式研究集会  (信州大学理学部) 

    Presentation date: 2018.06

  • 記憶型消散構造の数理解析と応用

    川島秀一

    熱エネルギー変換工学・数学融合研究所 第1回シンポジウム「工学と数学の融合に向けて」  (早稲田大学西早稲田キャンパス) 

    Presentation date: 2018.04

  • General theory for hyperbolic balance laws and application to a model system of viscoelastic fluid

    川島秀一

    「応用解析」研究会定例セミナー  (早稲田大学先進理工学部) 

    Presentation date: 2018.04

  • Memory effects for hyperbolic problems

    S. Kawashima

    理工総合研究所 重点研究領域「数理科学研究所」開設研究集会  (早稲田大学西早稲田キャンパス) 

    Presentation date: 2018.03

  • On a model system of complex fluid

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 KMMビル) 

    Presentation date: 2017.11

  • Dissipative structure for hyperbolic systems with memory

    川島秀一

    研究集会「保存則をもつ偏微分方程式に対する解の特異性および漸近挙動の研究」  (京都大学数理解析研究所) 

    Presentation date: 2017.06

  • Decay property for hyperbolic systems with memory

    S. Kawashima

    Seminar at Tsinghua University  (Tsinghua University) 

    Presentation date: 2017.04

  • Dissipative structure of symmetric hyperbolic systems with memorytype dissipation

    S. Kawashima

    International Conference on Partial Differential Equations  (Silkroad Mathematics Center, Chinese Mathematical Society) 

    Presentation date: 2017.04

  • Dissipative structure for hyperbolic systems with memory-type dissipation

    川島秀一

    金沢解析セミナー  (金沢大学サテライト・プラザ) 

    Presentation date: 2017.03

  • Dissipative structure of symmetric hyperbolic systems with memorytype relaxation

    S. Kawashima

    PDE Colloquium in Konstanz  (University of Konstanz) 

    Presentation date: 2017.03

  • Decay property for hyperbolic systems with dissipation

    S. Kawashima

    Series of seminars at GSSI (Gran Sasso Science Institute) 

    Presentation date: 2017.02

  • Decay property for hyperbolic systems with memory-type Diffusion

    川島秀一

    「応用解析」研究会定例セミナー  (早稲田大学先進理工学部) 

    Presentation date: 2016.12

  • Mathematical analysis for hyperbolic balance laws

    S. Kawashima

    WinC-2016, Wayamba International Conference on Managing Systems from Source to Sink: Current Theories and Applications  (Wayamba University of Sri Lanka) 

    Presentation date: 2016.08

  • Dissipative structure for symmetric systems with memory-type dissipation

    川島秀一

    解析セミナー  (九州大学数理学研究院) 

    Presentation date: 2016.07

  • Discrete kinetic theory and hyperbolic balance laws

    S. Kawashima

    RIMS International Workshop 2016: Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics  (Kyoto University Clock Tower Centennial Hall) 

    Presentation date: 2016.05

  • Hyperbolic balance laws with relaxation

    S. Kawashima

    International Conference on Partial Differential Equations  (Zhejiang Normal University) 

    Presentation date: 2016.03

  • Diffusion waves for nonlinear partial Differential equations

    S. Kawashima

    Analysis Seminar  (National Cheng Kung University) 

    Presentation date: 2016.03

  • Hyperbolic balance laws with non-symmetric relaxation

    川島秀一

    松山解析セミナ2016  (愛媛大学) 

    Presentation date: 2016.02

  • 非線形消散構造の臨界性と非線形平面波の安定性

    川島秀一

    研究集会「数理モデルにおける非線型消散・分散構造の未開領域解明」  (仙台 東北大学数理科学記念館(川井ホール)) 

    Presentation date: 2016.01

  • Cattaneo型の熱弾性体方程式系について

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 小倉リーセントホテル) 

    Presentation date: 2015.11

  • Mathematical entropy and Euler-Maxwell system

    S. Kawashima

    International Workshop on the Multi-Phase Flow; Analysis, Modeling and Numerics  (Waseda University) 

    Presentation date: 2015.11

  • Mathematical entropy for hyperbolic balance laws with non-symmetric relaxation and its applications

    川島秀一

    非線形解析セミナー  (東京工業大学) 

    Presentation date: 2015.09

  • Mathematical entropy for hyperbolic balance laws and applications

    S. Kawashima

    第40回偏微分方程式論札幌シンポジウム  (北海道大学) 

    Presentation date: 2015.08

  • Non-isentropic Euler-Maxwell system in plasma physics and the corresponding mathematical entropy

    川島秀一

    偏微分方程式特別セミナー  (東北大学理学部) 

    Presentation date: 2015.07

  • Mathematical entropy and Euler-Cattaneo-Maxwell system

    S. Kawashima

    Fourth International Conference on Nonlinear Evolutionary Partial Differential Equations: Theories and Applications  (Shanghai Jiao Tong University) 

    Presentation date: 2015.06

  • Mathematical entropy and Euler-Cattaneo-Maxwell system

    S. Kawashima

    Analysis Seminar  (Institute of Mathematics, Academia Sinica) 

    Presentation date: 2015.05

  • Asymptotic profile of solutions to a hyperbolic Cahn-Hilliard equation

    S. Kawashima

    Colloquium  (Institute of Mathematics, Academia Sinica) 

    Presentation date: 2015.05

  • Mathematical analysis for hyperbolic systems of balance laws

    S. Kawashima

    Analysis Seminar  (Institute of Mathematics, Academia Sinica) 

    Presentation date: 2015.05

  • Asymptotic profile of solutions to a hyperbolic Cahn-Hilliard equation

    S. Kawashima

    Nanjing Conference on Dissipative Partial Differential Equations  (Nanjing University of Aeronautics and Astronautics) 

    Presentation date: 2015.04

  • Asymptotic profile of solutions to a hyperbolic Cahn-Hilliard equation

    S. Kawashima

    PDE seminar  (Chinese University of Hong Kong) 

    Presentation date: 2015.04

  • Dissipative structure and nonlinear stability for the dissipative Timoshenko system

    森直文

    日本数学会年会  (明治大学駿河台キャンパス) 

    Presentation date: 2015.03

  • Timoshenko系の非線形安定性に関する最近の進展

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 小倉リーセントホテル) 

    Presentation date: 2014.11

  • Dissipative structure and nonlinear stability for the Timoshenko system

    S. Kawashima

    PDE seminar  (City University of Hong Kong) 

    Presentation date: 2014.11

  • Asymptotic profiles of solutions to some hyperbolic type equations

    S. Kawashima

    PDE seminar  (Chinese University of Hong Kong) 

    Presentation date: 2014.11

  • Global existence and optimal decay of solutions to the dissipative Timoshenko system

    川島秀一

    微分方程式セミナー  (大阪大学理学部) 

    Presentation date: 2014.11

  • Global existence and optimal decay of solutions with minimal regularity for the dissipative Timoshenko system

    川島秀一

    弘前解析セミナー  (弘前大学理工学部) 

    Presentation date: 2014.10

  • Decay property for the Timoshenko system with thermal effects: Cattaneo versus Fourier's law

    森直文

    日本数学会秋季総合分科会  (広島大学) 

    Presentation date: 2014.09

  • Dissipative structure for general systems of partial Differential equations with relaxation

    S. Kawashima

    Wayamba International Conference WinC-2014  (Wayamba University of Sri Lanka) 

    Presentation date: 2014.08

  • Dissipative structure for symmetric hyperbolic systems with relaxation

    S. Kawashima

    SPS-DFG Japanese-German Graduate Externship Kicko?Meeting  (Waseda University) 

    Presentation date: 2014.06

  • Asymptotic behavior of solutions to nonlinear partial Differential equations with dissipation

    川島秀一

    第3回偏微分方程式レクチャーシリーズ in 福岡工業大学  (福岡工業大学) 

    Presentation date: 2014.05

  • Open problems on the asymptotic profiles of solutions to a certain hyperbolic equation with dissipation

    川島秀一

    解析セミナー  (九州大学数理学研究院) 

    Presentation date: 2014.04

  • Asymptotic profiles of solutions to some hyperbolic type equations

    川島秀一

    熊本大学応用解析セミナー  (熊本大学) 

    Presentation date: 2014.02

  • Asymptotic behavior of solutions to some hyperbolic type equations

    川島秀一

    平成25年度藤田保健衛生大学数理講演会  (豊明市 藤田保健衛生大学病院外来棟) 

    Presentation date: 2014.02

  • ある高階の双曲型方程式について

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 KMMビル) 

    Presentation date: 2013.11

  • Asymptotic behavior of solutions to the generalized cubic double dispersion equation

    S. Kawashima

    RIMS Workshop: Kinetic Modeling and Related Equations: Conference in Memory of Seiji Ukai  (Rakuyu Kaikan) 

    Presentation date: 2013.10

  • Asymptotic profile of solutions to the generalized cubic double dispersion equation

    川島秀一

    広島微分方程式研究会  (広島大学) 

    Presentation date: 2013.10

  • Dissipative structure for symmetric hyperbolic-parabolic systems with non-symmetric relaxation

    川島秀一

    数理モデルにおける非線型消散・分散構造の臨界性の未開領域解明-キックオフ・ミーティング in 山形-  (ヒルズサンピア山形) 

    Presentation date: 2013.07

  • Mathematical anaysis for systems of viscoelasticity and viscothermoelasticity

    S. Kawashima

    ERC-Numeriwaves Seminar  (BCAM) 

    Presentation date: 2013.03

  • Stationary solutions to the Euler-Maxwell system

    川島秀一

    北九州地区における偏微分方程式研究集会  (北九州 小倉リーセントホテル) 

    Presentation date: 2012.11

  • Decay property for systems of viscoelasticity and viscothermoelasticity

    S. Kawashima

    International Conference "Mathematical fluid Dynamics and Nonlinear Wave"  (Waseda University) 

    Presentation date: 2012.08

  • Dissipative structure for symmetric hyperbolic systems

    S. Kawashima

    Workshop Nonlinear Waves and Their Stability  (University of Konstanz) 

    Presentation date: 2012.05

  • A short comment on the local existence for some nonlinear partial do?erential equations

    S. Kawashima

    PDE seminar  (Chinese University of Hong Kong) 

    Presentation date: 2012.03

  • Timoshenko系の消散構造

    川島秀一

    北九州地区における偏微分方程式研究集会  (九州工業大学) 

    Presentation date: 2011.11

  • Recent progress on the decay structure for symmetric hyperbolic systems

    S. Kawashima

    Seminar at Beijing University of Technology  (Beijing University of Technology) 

    Presentation date: 2011.10

  • 非対称な緩和項を持つ対称双曲型方程式系の減衰構造

    上田好寛

    日本数学会秋季総合分科会  (信州大学) 

    Presentation date: 2011.09

  • Decay estimates for quasi-linear hyperbolic systems of viscoelasticity

    P.M.N. Dharmawardane

    日本数学会秋季総合分科会  (信州大学) 

    Presentation date: 2011.09

  • Decay property of regularity-loss type for symmetric hyperbolic systems with relaxation

    S. Kawashima

    The 3rd Kyushu University-POSTECH Joint Workshop on Partial Differential Equations and fluid Dynamics  (POSTECH) 

    Presentation date: 2011.06

  • Decay property of regularity-loss type for symmetric hyperbolic systems with relaxation

    川島秀一

    広島数理解析セミナー  (広島大学) 

    Presentation date: 2011.05

  • Recent progress on the stability analysis for symmetric hyperbolic systems

    S. Kawashima

    Seminar at University of Paris VI  (University of Paris VI) 

    Presentation date: 2011.03

  • Recent progress on the stability analysis for symmetric hyperbolic systems

    川島秀一

    熊本大学理学部談話会  (熊本大学) 

    Presentation date: 2010.12

  • A new type decay structure for symmetric hyperbolic systems

    S. Kawashima

    International Conference on Nonlinear Partial Differential Equations: Mathematical Theory, Computation and Applications  (National University of Singapore) 

    Presentation date: 2010.11

  • Matsumura's technique and stability analysis

    S. Kawashima

    International Conference on Partial Differential Equations and Mathematical Physics  (Shirankaikan Annex) 

    Presentation date: 2010.11

  • A new type decay structure for symmetric hyperbolic systems

    川島秀一

    北九州地区における偏微分方程式研究集会  (九州工業大学) 

    Presentation date: 2010.11

  • Recent development on the stability analysis for symmetric hyperbolic systems

    川島秀一

    NAセミナー  (慶応大学数理科学科) 

    Presentation date: 2010.10

  • Global solutions to a quasi-linear dissipative plate equation

    Y. Liu

    日本数学会秋季総合分科会  (名古屋大学) 

    Presentation date: 2010.09

  • Existence of global solutions to quasilinear hyperbolic equations for viscoelasticity

    ダルマワルダネ マヘシ

    日本数学会秋季総合分科会  (名古屋大学) 

    Presentation date: 2010.09

  • Decay propery for some hyperbolic-type equations with dissipation

    川島秀一

    研究集会「流体と気体の数学解析」  (京都大学数理解析研究所) 

    Presentation date: 2010.07

  • Decay property for a quasi-linear dissipative plate equation

    S. Kawashima

    Fourth Workshop on Nonlinear Partial Differential Equations: Analysis, Computation and Applications  (National Taiwan University) 

    Presentation date: 2010.06

  • Asymptotic behavior of solutions to a model system of a radiating gas

    劉永琴

    日本数学会年会  (慶応大学) 

    Presentation date: 2010.03

  • Decay property for hyperbolic systems of viscoelasticity

    P.M.N. Dharmawardane

    日本数学会年会  (慶応大学) 

    Presentation date: 2010.03

  • On some hyperbolic-type equations with dissipation

    S. Kawashima

    Seminar at Department of Mathematics  (Politecnico di Torino) 

    Presentation date: 2010.03

  • Decay structure for systems of viscoelasticity

    S. Kawashima

    Mathematical Analysis on the Navier-Stokes Equations and Related Topics, Past and Future In memory of Professor Tetsuro Miyakawa  (神戸大学 瀧川記念学術会館) 

    Presentation date: 2009.12

  • Decay properties for hyperbolic equations

    川島秀一

    北九州地区における偏微分方程式研究集会  (九州工業大学) 

    Presentation date: 2009.11

  • Decay property for hyperbolic systems of viscoelasticity

    川島秀一

    偏微分方程式の諸問題  (東海大学理学部) 

    Presentation date: 2009.10

  • 偏微分方程式の消散構造とエネルギー減衰

    川島秀一

    京都大学数学教室談話会  (京都大学理学部) 

    Presentation date: 2009.10

  • Global existence and asymptotic behavior of solutions for quasilinear dissipative plate equation

    劉永琴

    日本数学会秋季総合分科会  (大阪大学) 

    Presentation date: 2009.09

  • Decay property for a dissipative plate equation

    川島秀一

    奈良女子大学偏微分方程式研究集会  (奈良女子大学理学部) 

    Presentation date: 2009.06

  • Hardyの不等式と安定性解析

    川島秀一

    東北大学数学教室談話会  (東北大学理学部) 

    Presentation date: 2009.06

  • Hardy type inequalities

    Presentation date: 2008.11

  • Hardy type inequality and application to the stability of degenerate stationary waves

    S. Kawashima

    Workshop Mathematical fluid Dynamics  (Tech Univ Darmstadt) 

    Presentation date: 2008.09

  • Hardy type inequality and application to the stability of degenerate stationary waves

    S. Kawashima

    Workshop Mathematical fluid Dynamics  (Tech Univ Darmstadt) 

    Presentation date: 2008.09

  • 半直線上の熱伝導圧縮性粘性流体の定常解に ついて

    中村徹

    日本数学会秋季総合分科会  (東京工業大学) 

    Presentation date: 2008.09

  • A Hardy type inequality and application to the stability of degenerate stationary waves

    川島秀一

    研究集会「流体と気体の数学解析」  (京都大学数理解析研究所) 

    Presentation date: 2008.07

  • Hardy type inequality and application to the stability of degenerate stationary waves

    S. Kawashima

    Seminar at National Chiao Tung University 

    Presentation date: 2008.03

  • 消散型移流波動方程式の多次元半空間における平面定 常波の安定性 (II)

    上田好寛

    日本数学会年会  (近畿大学理工学部) 

    Presentation date: 2008.03

  • 単独粘性保存則に対するある初期値境界値問題の 解の漸近評価について

    橋本伊都子

    日本数学会年会  (近畿大学理工学部) 

    Presentation date: 2008.03

  • 保存則系におけるエントロピーと消散構造

    川島秀一

    日本数学会年会  (近畿大学理工学部) 

    Presentation date: 2008.03

  • 消散構造を持つ非線形偏微分方程式系の解の漸近挙動

    川島秀一

    九州非線形偏微分方程式冬の学校  (九州大学理学部) 

    Presentation date: 2007.12

  • 第19回北九州地区における偏微分方程式研究会

    川島秀一

    Hardy type inequality and application  (西日本工業大学) 

    Presentation date: 2007.11

  • Drift-Diffusion model for semiconductor

    S. Kawashima

    DMHF 2007: COE Conference on the Development of Dynamic Mathematics with High Functionality  (Fukuoka Recent Hotel) 

    Presentation date: 2007.10

  • 消散型移流波動方程式の多次元半空間における平面定常波の安定性

    上田好寛

    日本数学会秋季総合分科会  (東北大学) 

    Presentation date: 2007.09

  • Existence of stationary solutions to drift-Diffusion model for a semiconductor

    小林遼

    日本数学会秋季総合分科会  (東北大学) 

    Presentation date: 2007.09

  • Stability of degenerate stationary waves for viscous conservation laws

    S. Kawashima

    The Second Workshop on Nonlinear Partial Differential Equations: Analysis, Computation and Application  (Seoul National University) 

    Presentation date: 2007.05

  • Asymptotic stability of stationary waves for viscous conservation laws

    川島秀一

    発展方程式シンポジウム  (東海大学湘南校舎) 

    Presentation date: 2007.03

  • 粘性気体に現れる縮退定常波の漸近安定性

    上田好寛

    日本数学会年会  (埼玉大学) 

    Presentation date: 2007.03

  • Drift-Diffusion型モデルの解の減衰評価と漸近挙動について

    小林遼

    日本数学会年会  (埼玉大学) 

    Presentation date: 2007.03

  • Asymptotic stability of stationary waves for viscous conservation laws

    S. Kawashima

    Workshop on Mathematical Analysis on Nonlinear Phenomena  (Keio University) 

    Presentation date: 2006.12

  • Stability of degenerate stationary waves for viscous gases

    川島秀一

    第4回浜松偏微分方程式研究集会  (静岡大学工学部) 

    Presentation date: 2006.12

  • Dissipative structure of regularity-loss type and applications

    S. Kawashima

    Eleventh International Conference on Hyperbolic Problems: Theory, Numerics and Applications  (E_cole Normale Sup_erieure de Lyon) 

    Presentation date: 2006.07

  • 非線形緩和的双曲型系の大域解の存在と解の漸近挙動

    上田好寛

    日本数学会年会  (中央大学) 

    Presentation date: 2006.03

  • Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system

    細野敬史

    日本数学会年会  (中央大学) 

    Presentation date: 2006.03

  • Dissipative structure of regularity-loss type and application to some nonlinear hyperbolic-elliptic system

    S. Kawashima

    Pusan-Kyushu Symposium on Partial Differential Equations  (Pusan National University) 

    Presentation date: 2006.01

  • Decay estimates at the consumption of regularity and its application to a nonlinear problem

    川島秀一

    広島微分方程式研究会  (広島大学) 

    Presentation date: 2005.10

  • 可微分性損失型エネルギー減衰評価とその応用

    川島秀一

    月曜解析セミナー  (東北大学) 

    Presentation date: 2005.10

  • Dissipative structure for hyperbolic systems

    S. Kawashima

    Workshop on Partial Differential Equations  (LNCC) 

    Presentation date: 2005.08

  • Dissipative structure for hyperbolic systems

    S. Kawashima

    Workshop on Partial Differential Equations  (LNCC) 

    Presentation date: 2005.08

  • Dissipative structure for hyperbolic systems

    S. Kawashima

    The Fourth International Conference on Nonlinear Analysis and Convex Analysis  (Okinawa Convention Center) 

    Presentation date: 2005.06

  • Stability of planar stationary solution of the compressible Navier-Stokes equation on the half space

    隠居良行

    日本数学会年会  (岡山大学) 

    Presentation date: 2005.03

  • 対称双曲系の消散構造

    川島秀一

    京都解析コロキウム  (京都大学) 

    Presentation date: 2005.01

  • 漸化式と微分方程式の安定性について

    川島秀一

    北九州地区における数学教育研究会  (西日本工業大学) 

    Presentation date: 2005.01

  • 双曲型方程式系の新しい消散構造

    川島秀一

    慶応義塾大学数理科学科談話会  (慶応義塾大学) 

    Presentation date: 2004.12

  • Decay estimates of solutions for second order hyperbolic systems with dissipation

    川島秀一

    広島微分方程式研究会  (広島大学) 

    Presentation date: 2004.10

  • Dissipative structure for symmetric hyperbolic systems

    S. Kawashima

    The 6th International Workshop on Mathematical Aspects of fluid and Plasma Dynamics  (Kyoto University) 

    Presentation date: 2004.09

  • Dissipative structure for symmetric hyperbolic systems

    川島秀一

    中央大学・偏微分方程式セミナー  (中央大学) 

    Presentation date: 2004.05

  • Lp energy method for viscous conservation laws

    川島秀一

    早稲田大学・応用解析セミナー  (早稲田大学) 

    Presentation date: 2003.12

  • Hyperbolic balance laws and entropy

    S. Kawashima

    Seminar at IMPA 

    Presentation date: 2003.11

  • Entropy and symmerization

    川島秀一

    第15回北九州地区における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 2003.11

  • Hyperbolic balance laws and entropy

    川島秀一

    研究集会「流体と気体の数学解析」  (京都大学数理解析研究所) 

    Presentation date: 2003.07

  • Hyperbolic balance laws and entropy

    川島秀一

    熊本大学・応用解析セミナー  (熊本大学) 

    Presentation date: 2003.05

  • Dissipative structure and entropy for hyperbolic systems of balance laws

    S. Kawashima

    Workshop on Multiphase fluid Flows and Multi-Dimensional Hyperbolic Problems  (Isaac Newton Institute) 

    Presentation date: 2003.03

  • Asymptotic stability of planar waves for viscous conservation laws in Rn+ : Lp approach and the rate of convergence

    S. Kawashima

    Seminar at University of Heidelberg 

    Presentation date: 2003.02

  • Asymptotic stability of planar waves for viscous conservation laws in Rn+

    S. Kawashima

    Seminar at University of L'Aquila 

    Presentation date: 2002.11

  • Lp energy method for viscous conservation laws

    川島秀一

    第14回北九州地区における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 2002.11

  • Stability of planar waves for viscous conservation laws in n-dimensional half space

    川島秀一

    早稲田大学・応用解析セミナー  (早稲田大学) 

    Presentation date: 2002.06

  • Nonlinear Diffusion waves for viscous conservation laws in half space

    S. Kawashima

    Seminar at Academia Sinica 

    Presentation date: 2002.03

  • Stability of planar waves for viscous conservation laws in Rn+

    S. Kawashima

    Seminar at National Taiwan University 

    Presentation date: 2002.03

  • Asymptotic stability of nonlinear Diffusion waves for viscous conservation laws in the half space

    川島秀一

    小倉における偏微分方程式研究集会  (九州工業大学) 

    Presentation date: 2002.02

  • Nonlinear waves for viscous conservation laws in the half space

    川島秀一

    第12回北九州地区における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 2000.11

  • Nonlinear waves for a viscous conservation laws in the half space

    S. Kawashima

    Seminar at Chinese Academy of Sciences 

    Presentation date: 2000.10

  • Nonlinear waves for a viscous conservation laws in the half space

    S. Kawashima

    Seminar at Fudan University 

    Presentation date: 2000.10

  • Stationary solutions to the discrete Boltzmann equation in the half space

    S. Kawashima

    Seminar at Institute of Applied Physics and Computational Mathematics 

    Presentation date: 2000.10

  • Existence and stability of stationary waves for the compressible Navier-Stokes equation in the half space

    S. Kawashima

    Workshop on Partial Differential Equations, Thermo & Visco & Elasticity  (University of Konstanz) 

    Presentation date: 2000.07

  • Existence and stability of stationary solutions for the discrete Boltzmann equation in the half space

    S. Kawashima

    Symposium on Nonlinear Partial Differential Equations  (Technical University of Wien) 

    Presentation date: 2000.03

  • Nonlinear waves for a viscous gas in the half space

    S. Kawashima

    Eighth International Conference on Nonlinear Hyperbolic Problems  (University of Magdeburg) 

    Presentation date: 2000.02

  • 半空間における粘性気体の非線形波

    川島秀一

    日本数学会九州支部例会  (九州大学) 

    Presentation date: 2000.02

  • Nonlinear waves for the compressible Navier-Stokes equation in the halfspace

    川島秀一

    第11回北九州地区における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 1999.11

  • 圧縮性 Navier-Stokes 方程式の半空間における定常解の漸近安定性

    川島秀一

    早稲田大学・応用解析セミナー  (早稲田大学) 

    Presentation date: 1999.06

  • Half-space problem for the discrete Boltzmann equation

    川島秀一

    北九州における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 1998.11

  • Survey on the initial-boundary value problems for the discrete Boltzmann equation

    S. Kawashima

    21st International Symposium on Rared Gas Dynamics 

    Presentation date: 1998.07

  • On the stability of stationary solutions to the discrete Boltzmann equation in the half space

    川島秀一

    研究集会「第3回流体力学の数学解析」  (京都大学) 

    Presentation date: 1998.07

  • Asymptotic stability of nonlinear waves for a model system of a radiating gas

    S. Kawashima

    Special Program on Partial Differential Equations  (City University of Hong Kong) 

    Presentation date: 1998.03

  • Survey on the initial-boundary value problems for the discrete Boltzmann equation

    S. Kawashima

    Special Program on Partial Differential Equations  (City University of Hong Kong) 

    Presentation date: 1998.03

  • Hyperbolic conservation laws coupled with elliptic equations

    S. Kawashima

    7th International Conference on Hyperbolic Problems  (ETH Zentrum Zurich) 

    Presentation date: 1998.02

  • 離散ボルツマン方程式の初期・境界値問題(Initial-boundary value problems for the discrete Boltzmann equation)

    川島秀一

    双曲系の諸問題研究集会  (大阪電気通信大学) 

    Presentation date: 1998.02

  • 輻射気体のモデル方程式の非線形波

    川島秀一

    Workshop on Mathematical Analysis for Nonlinear Phenomena  (慶応大学) 

    Presentation date: 1998.01

  • On hyperbolic-elliptic coupled systems in radiation hydrodynamics

    川島秀一

    北九州における偏微分方程式研究会  (西日本工業大学) 

    Presentation date: 1997.11

  • 非線形双曲・楕円型連立方程式の大域解の存在と漸近挙動および解の近似について

    新国淑子

    日本数学会秋季総合分科会  (東京大学) 

    Presentation date: 1997.10

  • 熱放射を考慮した気体の方程式の衝撃波について

    西畑伸也

    日本数学会秋季総合分科会  (東京大学) 

    Presentation date: 1997.10

  • Weak solutions with a shock for a model system of the radiating gas

    西畑伸也

    応用数学シンポジウム  (城西大学) 

    Presentation date: 1997.09

  • Stability of nonlinear waves for a model system of a radiating gas

    S. Kawashima

    Workshop on Analysis of Conservation Laws 

    Presentation date: 1997.08

  • Hyperbolic-elliptic coupled systems

    S. Kawashima

    Summerschool on Analysis of Conservation Laws 

    Presentation date: 1997.08

  • Shock waves for a model system of the radiating gas

    S. Kawashima, S. Nishibata

    Workshop on Partial Differential Equations  (IMPA) 

    Presentation date: 1997.07

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Syllabus

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Committee Memberships

  • 2012.04
    -
    2015.03

    日本数学会  教育研究資金問題検討委員会委員

  • 2012.04
    -
    2013.03

    日本学術振興会  科学研究費委員会専門委員

  • 2003.04
    -
    2013.03

    日本数学会  解析学賞委員

  • 2008.04
    -
    2009.03

    日本学術振興会  科学研究費委員会専門委員

  • 2003.04
    -
    2007.03

    日本数学会  受賞候補推薦委員

  • 2003.04
    -
    2006.03

    日本数学会  評議員

  • 2001.04
    -
    2006.03

    日本数学会  委員

  • 2002.04
    -
    2003.03

    日本学術振興会  特別研究員等審査会専門委員

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    日本数学会  解析学賞委員会 委員長

  •  
     
     

    日本数学会  解析学賞推薦委員

  •  
     
     

    日本数学会  解析学賞推薦委員

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