Updated on 2023/09/30

写真a

 
KITA, Kosuke
 
Affiliation
Faculty of Science and Engineering, School of Advanced Science and Engineering
Job title
Assistant Professor(non-tenure-track)
Degree
Doctor of Science ( 2022.03 Waseda University )
Mail Address
メールアドレス
Homepage URL
http://kkitawap.starfree.jp/index_e.html

Research Experience

  • 2022.04
    -
    Now

    Waseda University   Faculty of Science and Engineering

  • 2020.04
    -
    2022.03

    日本学術振興会 特別研究員 DC2

Education Background

  • 2019.04
    -
    2022.03

    Waseda University   Graduate School of Advanced Science and Engineering  

  • 2017.04
    -
    2019.03

    Waseda University   Graduate School of Advanced Science and Engineering  

  • 2013.04
    -
    2017.03

    Waseda University   School of Advanced Science and Engineering  

Professional Memberships

  • 　
    　
    　

    日本数学会

Research Areas

  • Basic analysis   函数解析学 / Mathematical analysis   函数方程式論

Research Interests

  • 非線形発展方程式

  • 偏微分方程式

  • 非線形境界条件

  • 解の定性的理論

Awards

  • 小泉賞

    2019.03   早稲田大学 応用物理会・物理会  

 

Papers

  • A remark on the blowing up of solutions to Nakao's problem

    Kosuke Kita, Ryunosuke Kusaba

    Journal of Mathematical Analysis and Applications   513 ( 1 ) 126199 - 126199  2022.09  [Refereed]

    DOI

    Scopus

  • On a comparison theorem for parabolic equations with nonlinear boundary conditions

    Kosuke Kita, Mitsuharu Ôtani

    Advances in Nonlinear Analysis   11 ( 1 ) 1165 - 1181  2022.03  [Refereed]

    　View Summary

    Abstract

    In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Bounds for global solutions of nonlinear heat equations with nonlinear boundary conditions

    Libertas Mathematica (new series)   41 ( 1 ) 1 - 22  2021  [Refereed]

    DOI

  • Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions

    Kosuke Kita, Mitsuharu Ôtani

    Differential Equations & Applications   11 ( 2 ) 227 - 242  2019  [Refereed]

    DOI

  • On some parabolic systems arising from a nuclear reactor model with nonlinear boundary conditions

    Kosuke Kita, Mitsuharu Ôtani, Hiroki Sakamoto

    Advances in Mathematical Sciences and Applications   27 ( 2 ) 193 - 224  2018  [Refereed]

Presentations

  • On critical phenomena for nonlinear heat equations on bounded domains characterized by nonlinear boundary conditions

    Kosuke Kita  [Invited]

    The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications 

    Presentation date： 2023.06

    Event date：
    2023.05
    -
    2023.06

  • Mosco convergence of functionals associated with Laplacian under nonlinear boundary conditions

    日本数学会2023年度年会 

    Presentation date： 2023.03

  • Global existence and blow-up of solutions to nonlinear heat equations with nonlinear boundary conditions

     [Invited]

    Presentation date： 2023.02

  • Weighted L^∞ estimates for solutions to the damped wave equation in three space dimensions and its application

     [Invited]

    Presentation date： 2022.12

  • Weighted \(L^\infty\) estimates for solutions to the damped wave equation in three space dimensions

     [Invited]

    The Second One Day Workshop on Hyperbolic PDE in Kushiro 

    Presentation date： 2022.11

  • Existence and nonexistence of global solutions to nonlinear diffusion equations on a bounded domain

    Presentation date： 2022.09

  • Existence and nonexistence of global solutions to nonlinear diffusion equations with nonlinear boundary conditions

     [Invited]

    Presentation date： 2022.05

  • Existence and nonexistence of global solutions for nonlinear heat equations with nonlinear boundary conditions

     [Invited]

    Critical Exponent and Nonlinear Partial Differential Equations 2022 

    Presentation date： 2022.03

  • Existence and nonexistence of global solutions for nonlinear heat equations on a bounded domain

    The 18th Mathematics Conference for Young Researchers 

    Presentation date： 2022.03

  • Qualitative theory of solutions to parabolic equations with nonlinear boundary conditions

     [Invited]

    Presentation date： 2022.02

  • On the global existence and blow-up of solutions for nonlinear heat equations on bounded domains

    Presentation date： 2021.12

  • Convergence of functional associated with Laplacian under nonlinear boundary conditions

    Presentation date： 2021.08

  • 非線形境界条件を伴う非線形熱方程式に対する臨界現象について

    喜多 航佑  [Invited]

    One Day Workshop抽象発展方程式のこれまでとこれから -動的境界条件への応用を見据えて- 

    Presentation date： 2021.01

  • Comparison theorem for parabolic equations governed by nonlinear boundary conditions and its applications

     [Invited]

    International Workshop on Multiphase Flows: Analysis, Modelling and Numerics 

    Presentation date： 2020.12

  • Comparison theorem for parabolic equations governed by nonlinear boundary conditions and its applications

     [Invited]

    Presentation date： 2020.09

  • On some nonlinear heat equations with nonlinear boundary conditions of radiation type

     [Invited]

    Presentation date： 2020.05

  • A bound for global solutions of some parabolic equation with nonlinear boundary conditions

    Presentation date： 2019.12

  • On some parabolic equations with nonlinear boundary conditions of radiation type

     [Invited]

    Presentation date： 2019.11

  • On the uniform boundedness for global solutions of nonlinear heat equations with nonlinear boundary conditions in bounded domain

    Presentation date： 2019.09

  • 非線形境界条件を伴う非線形熱方程式の大域解の有界性について

    Presentation date： 2019.08

  • On the comparison theorem for parabolic equations governed by nonlinear boundary conditions

    日本数学会2019年度年会 

    Presentation date： 2019.03

  • An abstract comparison theorem for parabolic equations governed by nonlinear boundary conditions

    Presentation date： 2019.03

  • 非線形境界条件に支配される放物型方程式に対する比較定理とその応用について

    The 15th Mathematics Conference for Young Researchers 

    Presentation date： 2019.03

  • 非線形境界条件に支配される放物型方程式の初期値境界値問題に対する比較定理とその応用

    第44回発展方程式研究会 

    Presentation date： 2018.12

  • Bounds for global solutions of a reaction diffusion system

    日本数学会2018年度秋季総合分科会 

    Presentation date： 2018.09

  • The uniform boundedness of global solutions for a reaction diffusion system

    第40回発展方程式若手セミナー 

    Presentation date： 2018.08

  • On some parabolic systems arising from a nuclear reactor model with nonlinear boundary conditions

     [Invited]

    12th AIMS Conference Series on Dynamical Systems and Differential Equations 

    Presentation date： 2018.07

  • Some threshold property for a reaction diffusion system arising from a nuclear reactor model

    日本数学会2018年度年会 

    Presentation date： 2018.03

  • Blow-up solutions for some parabolic systems arising from a nuclear reactor model

    第25回応用解析研究会シンポジウム 

    Presentation date： 2018.03

  • 原子炉モデルに因る或る反応拡散系に対する解の時間大域挙動の閾値に就いて

    第43回発展方程式研究会 

    Presentation date： 2017.12

  • On some parabolic systems arising from a nuclear reactor model

     [Invited]

    Theory of Evolution Equation and Mathematical Analysis of Nonlinear Phenomena 

    Presentation date： 2017.10

  • On some elliptic systems arising from a nuclear reactor model

    日本数学会2017年度秋季総合分科会 

    Presentation date： 2017.09

  • 原子炉モデルに起因するある反応拡散系について

    第39回発展方程式若手セミナー 

    Presentation date： 2017.09

  • 非線型境界条件を持つある反応拡散系の定常問題

    第24回応用解析研究会シンポジウム 

    Presentation date： 2017.03

▼display all

Research Projects

  • 拡散構造を持たない消散型波動方程式に対する大域可解性の理論の新展開

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up

    Project Year :

    2022.08
    -
    2024.03
     

  • Global existence of solutions to Nakao's problem

    Project Year :

    2022.10
    -
    2023.03
     

  • 非線形境界条件を伴う反応拡散方程式系の数学解析

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

    Project Year :

    2020.04
    -
    2022.03
     

Misc

  • 非線形境界条件を伴う非線形熱方程式の大域解の有界性について

    喜多 航佑

    第41回発展方程式若手セミナー報告集     259 - 264  2020

    Article, review, commentary, editorial, etc. (other)  

  • 非線形境界条件に支配される放物型方程式に対する比較定理とその応用について

    Hokkaido University technical report series in Mathematics   176   319 - 324  2019

  • On some parabolic systems arising from a nuclear reactor model (Theory of Evolution Equation and Mathematical Analysis of Nonlinear Phenomena)

    Kita, Kosuke

    RIMS Kokyuroku   2090   42 - 59  2018.09

    CiNii

  • The uniform boundedness of global solutions for a reaction diffusion system

    喜多 航佑

    第40回発展方程式若手セミナー報告集     121 - 128  2018

    Article, review, commentary, editorial, etc. (other)  

  • 原子炉モデルに起因するある反応拡散系について

    喜多 航佑

    第39回発展方程式若手セミナー報告集     125 - 134  2017

    Article, review, commentary, editorial, etc. (other)  

 

Syllabus

▼display all

Teaching Experience

  • 一般位相演習A

    Tokyo University of Science  

    2023.04
    -
    Now
     

  • 理工学基礎実1A・1B

    Waseda University  

    2022.04
    -
    Now
     

  • 物理学演習B / 応用物理学演習

    Waseda University  

    2022.04
    -
    Now
     

  • 数学演習 (物理/応物)

    Waseda University  

    2022.04
    -
    Now
     

 

Internal Special Research Projects

  • Global existence of solutions to Nakao's problem

    2022  

    　View Summary

    波動方程式と消散型波動方程式の連立系の初期値問題に対する時間大域解の存在についての研究を行った．消散型波動方程式は波動方程式と同じ双曲型偏微分方程式に分類されるが，その解は漸近挙動の観点から放物型偏微分方程式である熱方程式に近いと考えられる．上述の連立系は双曲型と放物型の間に横たわる階層構造を解明する為に考察すべき問題として提唱され「中尾の問題」と呼ばれている．本研究では単独の消散型波動方程式に対して解の重み付きの評価を新たに導出し，その応用として空間3次元の中尾の問題の時間大域解の存在を証明した．