Research theme for competitive and other funds (10)：
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
2004 - 2005 活性・抑制型反応拡散方程式系の定常解構造に関する研究
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 III: General case. Discrete and Continuous Dynamical Systems S. 2024. 17. 742-761
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. 178. 1-45
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
Spreading phenomenon in a nonlinear Stefan problem with a certain class of multistable nonlinearity
(International Conference on Elliptic and Parabolic Problems: GAETA 2024 2024)
Nonlinear Stefan problem with a certain class of multi-stable nonlinearity
(Euro-Japanese Conference on Nonlinear Diffusions 2023)
Nonlinear Stefan problem with a certain class of multi-stable nonlinearity
(ICIAM 2023 2023)
Logarithmic shiftings of a radial propagating terrace in a free boundary problem for a multi-stable reaction diffusion equation in high space dimensions
(The 13th AIMS conference on Dynamical Systems, Differential Equations and Applications 2023)
Nonlinear Stefan problem with a certain class of multi-stable nonlinearity
(The 13th AIMS conference on Dynamical Systems, Differential Equations and Applications 2023)
