Nakamura Makoto

Affiliation and department：
Job title： Professor

Research keywords (5)： Partial differential equations , Klein-Gordon equation , Schrodinger equation , wave equation , nonlinear

Research theme for competitive and other funds (28)：

2024 - 2027 曲がった時空中における偏微分方程式の爆発解に関する研究
2022 - 2025 相対論的流体方程式の研究
2018 - 2023 分散型方程式の時空間評価と非線形問題への応用に関する研究
2021 - 2022 発展型偏微分方程式における高精度数値計算手法の構築
2016 - 2021 解析学に基づくアインシュタイン方程式の総合研究

2018 - 2021 分散型方程式の時空間評価と非線形問題への応用に関する研究

2016 - 2020 解析学に基づくアインシュタイン方程式の総合研究

2018 - 2020 Research for the Cauchy problem for nonlinear Klein-Gordon equations in homogeneous and isotropic spaces

2013 - 2017 Well-poshness and asymptotic behaviour of solutions to nonlinear partial differential equations describing interaction between several fields

2012 - 2017 Mathematical Theory of turbulence by the method of modern analysis and computational science

2012 - 2016 Global behavior for nonlinear wave

2011 - 2015 Research on initial and boundary value problems, and space-time estimates for nonlinear partial differential equations

2009 - 2014 On analysis of interacting nonlocal waves

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

2011 - 2013 On geometric analysis related to the Cosmic Censorship Conjecture

2008 - 2012 Theory of global well-posedness on the nonlinear partial differential equations

2009 - 2011 Mathematical analysis of nonlinear partial differential equations describing interaction of several fields

2007 - 2010 Initial and boundary value problems for nonlinear dispersive wave equations

2005 - 2008 Study of free probability and operator algebras based on random matrices

2003 - 2007 United theory of existence of global solution and its asymptotic behavior to the nonlinear partial differential equations

2003 - 2006 Reseach for the singularities and regularity of solutions to crtical nonlinear partial differential equations

2004 - 2005 非線形波動方程式系のディリクレ条件下での外部問題

2002 - 2003 非線形クライン-ゴルドン方程式とベンジャミン-オノ方程式の時間大域可解性の研究

2001 - 2003 Characterizations of real Hardy spaces and functional analysis

2000 - 2002 Numerical Analysis for Inverse Problems and Applications of Wavelet Analysis

2000 - 2001 自由確率変数の作用素論的研究

1997 - 2000 Functional analytic study on global structures of nonlinear fields

1998 - 1998 非線型シュレディンガー方程式のソボレフ空間Hn/2(IRn)における初期値適正問題

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Papers (73)：

M. Nakamura. The Cauchy problem for a semilinear ordinary differential equation in the homogeneous and isotropic spacetime. Tsukuba Journal of Mathematics. 2023. 47. 153-189
Mikio Ichimiya, Makoto Nakamura. On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime. Evolution Equations and Control Theory. 2023. 12. 6. 1602-1628
Takuya Tsuchiya, Makoto Nakamura. Numerical accuracy and stability of semilinear Klein-Gordon equation in de Sitter spacetime. JSIAM Letters. 2023. 15. 45-48
Makoto Nakamura. The Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime. Journal of Mathematical Physics. 2021. 62. 12. 121509-121509
Makoto Nakamura, Hiroshi Takeda. Asymptotic behaviors of global solutions for a semilinear diffusion equation in the de Sitter spacetime. Asymptotic Analysis. 2021. 125. 3-4. 203-245

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MISC (1)：

Tsukasa Iwabuchi, Makoto Nakamura. SMALL SOLUTIONS FOR NONLINEAR HEAT EQUATIONS, THE NAVIER-STOKES EQUATION, AND THE KELLER-SEGEL SYSTEM IN BESOV AND TRIEBEL-LIZORKIN SPACES. ADVANCES IN DIFFERENTIAL EQUATIONS. 2013. 18. 7-8. 687-736

Books (4)：

The Cauchy problem for dissipative wave equations with weighted nonliner terms
Birkhauser 2019
半線形消散型波動方程式の Cauchy 問題の解の時間大域的漸近挙動
大学院GP数学レクチャーノートシリーズ,GP-TML20,東北大学大学院理学研究科発行, 2010
Einstein 方程式の初期値問題
東北大学グローバルCOE「物質階層を紡ぐ科学フロンティアの新展開」,春の学校「アインシュタイン方程式の世界観」偏微分方程式の幾何学的構造と物理的意味を求めて,講義録 2009
Modulation空間とその応用について
大学院GP数学レクチャーノートシリーズ,GP-TML7,東北大学大学院理学研究科発行 2008

Lectures and oral presentations (89)：

Blowing-up solutions for semi-linear Klein-Gordon equations in FLRW spacetimes
(2024)
Global solutions for semi-linear Klein-Gordon equations in FLRW spacetimes
(2024)
On the convergence and asymptotic behavior of the solution of semilinear Klein-Gordon equation
(2024)
Remarks on global solutions on semilinear Klein-Gordon equations in Friedmann-Lemaitre-Robertson-Walker spacetimes
(Mathematical Physics Seminar, The University of Texas Rio Grande Valley 2024)
On the Klein-Gordon equation under the quartic potential in the de Sitter spacetime
(Workshop on Nonlinear Hyperbolic PDEs, Tohoku University, Sendai 2023)

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Work history (1)：

2022/04 - 現在 Osaka University Graduate School of Information Science and Technology Professor

Committee career (6)：

2023/08 - 2023/08 国際研究集会 ``Beijing-Osaka joint workshop for PDE and related topics," 組織者(他1名)
2023/07 - 2023/07 国際研究集会 ``The 14th International ISAAC Congress,'' 組織者(他2名)
2022/08 - 2022/08 研究集会``Dispersive and wave equations,'' 組織者
2022/08 - 2022/08 International Conference ``Mathematical Analysis of Nonlinear Dispersive and Wave Equations,'' 代表組織委員(他組織者7名)
2021/12 - 2021/12 研究集会``Nonlinear Wave Equations,'' 組織者(他2名)

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