Ishige Kazuhiro

イシゲカズヒロ | Ishige Kazuhiro

Affiliation and department：
Job title： Professor
Homepage URL (2)： http://db.tohoku.ac.jp/whois/detail/cd1d714c5912bbb856be46ffe3cec71c.html , http://db.tohoku.ac.jp/whois/e_detail/cd1d714c5912bbb856be46ffe3cec71c.html

Research field (1)： Mathematical analysis

Research keywords (3)：半線形熱方程式の爆発問題 , 熱方程式の解の最大点 , 拡散方程式

Research theme for competitive and other funds (26)：

2024 - 2029 楕円型方程式の精密解析と定性理論の新展開
2020 - 2024 Development of the theory of diffusion equations for analysis on data separation
2019 - 2024 Systematical geometric analysis and asymptotic analysis for evolution equations
2019 - 2024 優臨界・臨界・劣臨界楕円型方程式の解構造の総合的研究
2018 - 2024 Development of the theory of diffusion equations for analysis on data separation

2020 - 2023 Asymptotic expansions of ODE type solutions and their related inverse problems

2020 - 2023 Invention and explorer for undiscovered structure and principle in the mathematical analysis for the relation between fluid dynamics and combustion.

2017 - 2022 Analysis of singular nonlinear structure in dissipative systems

2015 - 2020 Fusion and evolution of asymptotic analysis and geometric analysis in partial differential equations

2014 - 2018 Geometry of solutions of partial differential equations and the inverse problems accompanied by it

2013 - 2018 Elucidations on unexplored regions of problems related to the criticality of nonlinear dissipative and dispersive structures in mathematical models

2013 - 2018 非線形発展方程式の未踏臨界構造の解明

2012 - 2017 Geometry of moduli spaces for low dimensional manifolds

2013 - 2016 Parabolic concavity of solutions of parabolic equations

2011 - 2016 Geometric properties and asymptotic behavior of solutions of diffusion equations

2011 - 2016 Fundamental theory for viscosity solutions of fully nonlinear equations and its applications

2011 - 2015 Unified investigation on elliptic and parabolic equations

2012 - 2014 Towards de Giorgi-Nash-Moser theory on non-linear non-local partial differential equations.

2008 - 2013 Research for Critical Asymptotic Structure of Nonlinear Evolution Equations

2011 - 2012 Qualitative properties for the Laplace equation with a dynamical boundary condition

1997 - 2000 Research on well-posedness for the Navier-Stokes equations

1998 - 1998 熱方程式の解の一意性、及び非一意性について

1997 - 1998 Structure of positive solutions to second order elliptic and parabolic partial differential equations

1996 - 1996 逆問題と情報科学

1995 - 1995 応用偏微分方程式の数値シミュレーション

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Papers (85)：

Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige, Robert Laister. Local solvability and dilation-critical singularities of supercritical fractional heat equations. Journal de Mathématiques Pures et Appliquées. 2024. 186. 150-175
Kazuhiro Ishige. Eventual concavity properties of the heat flow. Mathematische Annalen. 2024. 390. 4. 5883-5922
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu. Characterization of F-concavity preserved by the Dirichlet heat flow. 2024
Kazuhiro Ishige, Sho Katayama. Supercritical Hénon-type equation with a forcing term. Advances in Nonlinear Analysis. 2024. 13. 1
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami. Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data. Zeitschrift für angewandte Mathematik und Physik. 2023. 74. 4

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MISC (6)：

Ishige Kazuhiro, Ishiwata Michinori. Global Solutions for a Semilinear Heat Equation in the Exterior Domain of a Compact Set (Geometric Aspect of Partial Differential Equations and Conservation Laws). 2013. 1842. 1-17
石毛和弘. 熱方程式の解の最大点挙動について. 応用数理. 2010. 20. 2. 25-36
Ishige Kazuhiro, Kawakami Tatsuki. On the Heat Equation in a Half-Space with a Nonlinear Boundary Condition (Variational Problems and Related Topics). RIMS Kokyuroku. 2009. 1671. 128-145
Kazuhiro Ishige, Yoshitsugu Kabeya. Large time behaviors of hot spots for the heat equation with a potential (vol 244, pg 2934, 2008). JOURNAL OF DIFFERENTIAL EQUATIONS. 2008. 245. 8. 2352-2354
Ishige Kazuhiro, Kabeya Yoshitsugu. Decay Rates of the Derivatives of the Solutions of the Heat Equations and Related Topics(Variational Problems and Related Topics). RIMS Kokyuroku. 2007. 1528. 12-35

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Lectures and oral presentations (17)：

Dirichlet heat flow による凸性保存について
(東北大学大学院理学研究科数学専攻談話会 2024)
Preservation of concavity properties by the Dirichlet heat flow
(Korean--Japanese workshop on elliptic and parabolic equations 2024)
Supersolutions of nonlinear parabolic systems and their applications
(Partial Differential Equations and Related Topics 2016)
Supersolutions of nonlinear parabolic systems and their applications
(7th Euro-Japanese Workshop on Blow-up 2016)
Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition
(3rd Chile-Japan Workshop on Nonlinear PDEs 2015)

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Professional career (1)：

博士(理学) (Tokyo Institute of Technology)

Committee career (8)：

2018/04 - 現在日本数学会理事
2015/04 - 2025/03 日本数学会函数方程式論分科会委員
2022/04 - 2024/03 日本数学会函数方程式論分科会評議員
2017/04 - 2020/03 日本数学会函数方程式論分科会評議員
2012/04 - 2013/03 日本数学会東北支部連絡責任評議員

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Awards (3)：

2014/09 - 日本数学会日本数学会解析学賞線形および非線形熱方程式の解の定性的解析
2010/12 - 日本数学会函数方程式分科会福原賞線形・非線形熱方程式の解の挙動の研究
1996/06 - 財団法人手島工業教育資金団手島記念研究賞非線形拡散方程式の解の挙動について

Association Membership(s) (1)：

日本数学会

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