Updated on 2025/04/04

写真a

 
KOIKE, Shigeaki
 
Affiliation
Faculty of Science and Engineering, School of Advanced Science and Engineering
Job title
Professor
Degree
理学(数学) ( Waseda University )

Research Experience

  • 2019.04
    -
    Now

    Waseda University   Faculty of Science and Engineering

  • 2012.04
    -
    2019.03

    東北大学   教授

  • 2006.04
    -
    2012.03

    埼玉大学大学院理工学研究科   教授

  • 1992.04
    -
    2002.03

    埼玉大学理学部   助教授

  • 1989.10
    -
    1992.03

    東京都立大学理学部   助手

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Education Background

  •  
    -
    1988.03

    Waseda University   Graduate School, Division of Science and Engineering  

  •  
    -
    1981.03

    Waseda University   Faculty of Science and Engineering   物理学科  

Committee Memberships

  • 2022.04
    -
    2023.03

    日本数学会  評議員

  • 2016.05
    -
    2016.10

    函数方程式論分科会  解析学賞選考委員

  • 2013.05
    -
    2013.10

    函数方程式論分科会  解析学賞選考委員

  • 2012.05
    -
    2012.10

    函数方程式論分科会  解析学賞選考委員長

Professional Memberships

  •  
     
     

    日本数学会

Research Areas

  • Basic analysis

Research Interests

  • 粘性解理論

  • Fully Nonlinear Partial Differential Equations

Awards

  • 解析学賞

    2016.09   日本数学会   完全非線形楕円型・放物型偏微分方程式のLp粘性解理論

    Winner: 小池茂昭

  • JMSJ Outstanding Paper Prize

    2010.03   日本数学会  

    Winner: 小池茂昭, Andrzej Swiech

 

Papers

  • Rate of Convergence for Approximate Solutions in Obstacle Problems for Nonlinear Operators

    Shigeaki Koike, Takahiro Kosugi

    Springer Proceedings in Mathematics & Statistics     63 - 93  2024.07

    DOI

    Scopus

  • Aleksandrov-Bakelman-Pucci maximum principle for Lp-viscosity solutions of equations with unbounded terms

    Shigeaki Koike, Andrzej Swiech

    Journal de Mathematiques Pures et Applquees   168 ( 9 ) 192 - 212  2022.12  [Refereed]

  • Regularity of solutions of obstacle problems -old &new-

    Shigeaki Koike

    Springer Proceedings in Mathematics & Statistics   346   205 - 243  2021.05  [Refereed]  [Invited]

  • On Lp-viscosity solutions of bilateral obstacles with unbounded ingredients

    Mathematische Annalen   377 ( 3-4 ) 833 - 910  2020.08  [Refereed]

  • Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications

    KOIKE Shigeaki, SWIECH Andrzej & TATEYAMA Shota

    Nonlinear Analysis   185   264 - 289  2019.08  [Refereed]

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Books and Other Publications

  • Nonlinear Partial Differential Equations for Future Applications

    Shigeaki Koike, Hideo Kozono, Takayoshi Ogawa, Shigeru Sakaguchi( Part: Edit)

    2021.05

  • 粘性解 -比較原理を中心に-

    小池 茂昭( Part: Sole author)

    2016.12

  • リメディアル数学

    泉屋周一他( Part: Joint author, 1章)

    数学書房  2011

  • 微分積分

    小池茂昭( Part: Sole author)

    数学書房  2010

  • International Conference for the 25th Anniversary of Viscosity Solutions

    Yoshikazu Giga 他( Part: Joint editor)

    学校図書  2008

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Presentations

  • ABP maximum principle with upper contact sets for fully nonlinear elliptic PDEs

    Shigeaki Koike  [Invited]

    OIST PDE seminar 

    Presentation date: 2022.12

    Event date:
    2022.12
     
     
  • Lp viscosity solution theory -revisited-

    KOIKE Shigeaki  [Invited]

    The 20th Northeastern Symposium on Mathematical Analysis 

    Presentation date: 2019.02

  • Obstacle problems for PDE of non-divergence type

    小池 茂昭  [Invited]

    研究集会「第14回 非線型の諸問題」 

    Presentation date: 2018.09

  • Recent development on Lp viscosity solutions for fully nonlinear parabolic PDE

    小池 茂昭  [Invited]

    九州における偏微分方程式研究集会 

    Presentation date: 2018.01

  • 自由境界問題の近似問題

    小池 茂昭  [Invited]

    室蘭非線形解析研究会 

    Presentation date: 2017.12

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Research Projects

  • 粘性解理論とその応用

    Project Year :

    1988.04
    -
    Now
     

  • Regularity theory for viscosity solutions of fully nonlinear equations and its applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2020.04
    -
    2025.03
     

  • New development of mathematical theory of turbulence by collaboration of the nonlinear analysis and computational fluid dynamics

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)

    Project Year :

    2016.05
    -
    2021.03
     

  • Evolution equations describing non-standard irreversible processes

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2016.04
    -
    2020.03
     

    Akagi Goro

     View Summary

    Irreversible phenomena represented by diffusion are major factors of important phenomena closely related to our life such as unidirectionality of time, aging of lives and fracture. Classical theories for irreversible phenomena have already been established in the last century. However, many important irreversible phenomena beyond the scope of the classical theories have been observed, and therefore, studies of mathematical analysis have been developed in order to analyze and understand those new phenomena. In this research project, we have developed a new framework on Evolution Equations for covering new mathematical models which describe various non-standard irreversible phenomena. In particular, principal methods of analysis have been established for phase-field equations with strong irreversibility arising from fracture and damage models as well as nonlocal evolution equations involving fractional Laplacians, and moreover, systematic research has been done for those equations.

  • New developments of the theory of viscosity solutions and its applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2016.04
    -
    2020.03
     

    Ishii Hitoshi

     View Summary

    This research builds on previous work to develop new developments in the theory and applications of viscosity solutions. The research has solved various problems in the theory and applications of viscosity solution theory, focusing on the basic theory of the comparison principle of solutions for differential and integral equations, unique existence and continuity of solutions, and applications to various asymptotic problems, optimal control, differential games, and geometric problems such as curvature flow, and has advanced the research on viscosity solution theory from both theoretical and applied perspectives. The results obtained have been used in natural science, engineering, society, and society. The results obtained are important as a fundamental theory for natural science, engineering, and social science.

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Misc

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Other

  • 粘性解の基礎理論の新展開

    2010.04
     
     

     View Summary

    Lp粘性解理論の研究

  • 完全非線形方程式の粘性解の基礎理論

    2008.04
     
     

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    完全非線形方程式のLp粘性解

  • 粘性解生誕25周年国際研究集会

    2007.04
     
     

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    上記研究集会の開催

  • 粘性解理論とその先端的応用

    2007.04
     
     

     View Summary

    粘性解理論の数理ファイナンスへの応用

  • 粘性解の微分可能性と最適制御に関する基礎研究

    2006.04
     
     

     View Summary

    粘性解の微分可能性を高めることで最適制御を決定する

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Syllabus

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Teaching Experience

  • Fourier Analysis

    Waseda University  

    2020.09
    -
    Now
     

  • Introduction of Mathematics B

    Waseda University  

    2020.09
    -
    Now
     

  • Topics in Mathematical Physics A

    Waseda University  

    2020.04
    -
    Now
     

  • Functional Analysis

    Waseda University  

    2020.04
    -
    Now
     

  • Ordinary Differential Equations

    Waseda University  

    2020.04
    -
    Now
     

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Social Activities

  • 仙台数学セミナー

    2014.08
     
     

     View Summary

    講演、演習を通して東北地方の高校生に数学の面白さを紹介する。

  • 出張講義

    2013.12
    -
     

     View Summary

    仙台一高で高校生に講義を行った。

Research Institute

  • 2022
    -
    2024

    Waseda Research Institute for Science and Engineering   Concurrent Researcher

Internal Special Research Projects

  • 超線形増大項のある完全非線形方程式の理論と応用

    2020  

     View Summary

    二階完全非線形一様楕円型方程式が1階微分項の増大度が1次以上の場合のABP最大値原理が成立するための十分条件は知られている。そこでは、逐次比較関数法を開発することで得られた。これらを利用して、平均場ゲームに現れる方程式系のうち粘性ハミルトン・ヤコビ方程式が低階項が一次以上の増大度がある場合の解の存在を導いた。

  • 臨界係数を持つ完全非線形方程式の粘性解のABP最大値原理とその応用に関する研究

    2019  

     View Summary

    完全非線形一様楕円型方程式が一階微分項に非有界係数μを持つ場合のABP最大値原理において、Lp粘性解に対しては、qが空間次元nより、大きいLq空間にμが属する時には、2007年の研究代表者の研究によって知られていた。しかし、強解に対してはμがLn空間に属していればが成り立つことが古典的な結果として、AleksandrovやBakelman等によって知られている。本研究では、Lp粘性解においてもμがLn空間に属する時に成立することを示すことを研究目的とした。研究成果としては、μがLnに属し、非斉次項fが次元nより大きいpの場合に示した。証明の鍵は、μがLnに属し、非斉次項がLpに属する時の対応する完全非線形方程式の強解の構成にある。