Research theme for competitive and other funds (9):
2021 - 2027 Quantitative analysis for nonlinear evolution equations of diffusion type
2020 - 2024 Propagation phenomena in reaction-diffusion equations involving nonlinear diffusion and multi-stable reaction term
2017 - 2020 数理生態学に現れる自由境界問題の解の形状と伝播現象の解明
2012 - 2013 自然科学に現れる非線形楕円型・放物型偏微分方程式に関する研究
2008 - 2013 空間非斉次性を含む反応拡散系の局在パターンのダイナミクスに関する研究
2011 - 2012 On a study on dynamics of localized pattern for a bistable reaction diffusion equations with a heterogeneous environment
2008 - 2009 On a study of a solution with a transition layer for a bistable reaction diffusion equation with a heterogeneous environment
2005 - 反応拡散方程式の定常解構造に関する研究
2005 - Stationary problem for reaction diffusion equations
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Papers (19):
Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada. A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions II: Asymptotic profiles of solutions and radial terrace solution. Journal de Mathematiques Pures et Appliquees. 2023
Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada. A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions III: General case. Discrete and Continuous Dynamical Systems. 2023
Hiroshi Matsuzawa, Mitsunori Nara. Asymptotic behavior of spreading fronts in an anisotropic multi-stable equation on $ \mathit{\boldsymbol{\mathbb{R}^N } } . Discrete and Continuous Dynamical Systems. 2022. 42. 10. 4707-4707
Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada. A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions I : Classification of asymptotic behavior. Discrete & Continuous Dynamical Systems. 2022. 42. 6. 2719-2745
Hiroshi Matsuzawa, Harunori Monobe, Masahiko Shimojo, Eiji Yanagida. Convergence to a traveling wave in the lgarithmic diffusion equation with a bistable nonlinearity. Indiana University Mathematics Journal. 2022. 71. 1. 125-151
Matsuzawa Hiroshi. Spreading speed and profile for nonlinear diffusion problems with free boundaries (Geometry of solutions of partial differential equations). RIMS Kokyuroku. 2014. 1896. 64-78
Kurata Kazuhiro, Matsuzawa Hiroshi. Multiple stable patterns in a balanced bistable equation with heterogeneous environments (Variational Problems and Related Topics). RIMS Kokyuroku. 2008. 1591. 134-142
Matsuzawa Hiroshi. On stationary solutions with transition layers for a bistable reaction diffusion equation. Memoirs of Numazu College of Technology. 2007. 41. 213-218
Matsuzawa Hiroshi. Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation(Mathematical Models of Phenomena and Evolution Equations). RIMS Kokyuroku. 2006. 1475. 107-120
Matsuzawa Hiroshi. Stable transition layers in a balanced bistable equation with degeneracy (Variational Problems and Related Topics). RIMS Kokyuroku. 2004. 1405. 155-174
Asymptotic profiles of solutions and propagating terrace for a free boundary problem of a multistable reaction-diffusion equation
(微分方程式の総合的研究 2019)
Asymptotic profiles of solutions and propagating terrace for free boundary problems of multistable reaction diffusion equations
(Qualitative Theory on Nonlinear Partial Differential Equations 2019)
Spreading and vanishing for a free boundary problem of a reaction diffusion equation with a multi-stable type nonlinearity in high space dimensions
(Recent Trends in Ordinary Differential Equations and Their Developments 2019)
Asymptotic profiles of solutions and propagating terrace for a free boundary problem of reaction diffusion equation with a nonlinearity of multi-stable type
(Mini Workshop on Reaction Diffusion Equations 2019)