# PUBLICATIONS

## Papers

- Yuki Kaneko, H.Matsuzawa and 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, 17(2024) 742--761
- Yuki Kaneko, H. Matsuzawa and 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, 178(2023) 1--45
- H. Matsuzawa and Mitsunori Nara, Asymptotic behavior of spreading fronts in an anisotropic multi-stable equation on $\mathbb{R}^N$, Discrete and Continuous Dynamical Systems, 42(2022) 4707--4740
- Yuki Kaneko, H. Matsuzawa and Yoshio Yamada, A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimension I : classification of asymptotic behavior, Discrete and Continuous Dynamical Systems, 42(2022) 2719--2745
- H. Matsuzawa, Harunori Monobe, Masahiko Shimojo and Eiji Yanagida, Convergence to a traveling wave in the logarithmic diffusion equation with a bistable nonlinearity, Indiana University Mathematics Journal 71 (2022), 125-151
- Yuki Kaneko, H. Matsuzawa and Yoshio Yamada, Asymptotic profiles of solutions and propagating terrace for a free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity, SIAM J. Math. Anal., 52(2020), 65-103
- Chengxia Lei, H. Matsuzawa, Rui Peng and Maolin Zhou, Refined estimates for the propagation speed of the transition solution to a free boundary problem with a nonlinearity of combustion type, Journal of Differential Equations, 265 (2018), 2897-2920.
- Yuki Kaneko, H. Matsuzawa, Spreading and vanishing in a free boundary problem for nonlinear diffusion equations with a forced given moving boundary, Journal of Differential Equations, 265(2018) 1000 - 1043.
- H. Matsuzawa, A free boundary problem for the Fisher-KPP equation with a given moving boundary, Communications on pure and applied analysis, 17(2018) 1821-1852
- Kosuke Kuto, H. Matsuzawa and Rui Peng, Concentration profile of the endemic equilibria of a reaction-diffusion-advection SIS epidemic model, Calculus of Variations and Partial Differential Equations 56, Article number: 112 (2017)
- Yuki Kaneko and H. Matsuzawa, Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations, J. Math. Anal. Appl., 428(2015) 43 - 76.
- Yihong Du, H. Matsuzawa and Maolin Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, Journal de Mathematiques Pures et Appliquees, 103(2015) 741-787.
- Yihong Du, H. Matsuzawa and Maolin Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal. 46(2014), Issue 1, 375-396
- Kazuhiro Kurata and H. Matsuzawa, Multiple stable patterns in a balanced bistable equation with heterogeneous environments. Appl. Anal. 89 (2010), no. 7, 1023-1035.
- Shin-Ichiro Ei and H. Matsuzawa, The motion of a transition layer for a bistable reaction diffusion equation with hererogeneous environment, Discrete and Continuous Dynamical Systems, 26(2010), no.3, 901-921.
- H. Matsuzawa, On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments, Discrete and Continuous Dynamical Systems supplement 2009, 516-525
- H. Matsuzawa, Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation, Electron. J. Diff. Eqns., Vol. 2006(2006), No. 05, 1-12.
- H. Matsuzawa, Asymptotic profiles of variational solutions for a FitzHugh-Nagumo type elliptic system, Nonlinear Analysis, Volume 63, Issues 5-7(2005), e2545-e2551
- H. Matsuzawa, Stable transition layers in a balanced bistable equation with degeneracy, Nonlinear Analysis, Theory Methods and Application, Volume 58, Issues 1-2(2004), 45-67
- H. Matsuzawa, Asymptotic profiles of variational solutions for a FitzHugh-Nagumo type elliptic system, Differential and Integral Equations, Volume 16, Number 8(2003), 897-926

## Preprint

- H. Matsuzawa and Tatsuya Ueno, Existence of ground state solutions to Kirchhoff--Schr\"{o}dinger system for subcritical and critical cases with nonconstant potentials in $\mathbb{R}^3$, in preparation

## Presentation(Oversea and international conferences)

- 22th, May. 2024, Spreading phenomenon in a nonlinear Stefan problem with a certain class of multistable nonlinearity, International Conference on Elliptic and Parabolic Problems: GAETA 2024, Gaeta, Italy
- 18th, October 2023, Nonlinear Stefan problem with a certain class of multi-stable nonlinearity, Euro-Japanese Conference on Nonlinear Diffusions, ICMAT-UAM, Madrid, Spain
- 25th, August 2023, Nonlinear Stefan problem with a certain class of multi-stable nonlinearity, ICIAM 2023, Tokyo
- 31th, May 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, University of North Carolina Wilmington, Wilmington , North Carolina, United States
- 31th, May 2023, Nonlinear Stefan problem with a certain class of multi-stable nonlinearity, The 13th AIMS conference on Dynamical Systems, Differential Equations and Applications, University of North Carolina Wilmington, Wilmington , North Carolina, United States
- 23th, November 2022, Nonlinear Stefan problem with a certain class of multi-stable nonlinearity, International Conference on Nonlinear Partial Differential Equations A celebration of Professor Yihong Du's 60th birthday, Sydney, Australia
- 24th, September 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, University of Science and Technology of China, Hefei, China.
- 11th, July 2019, Asymptotic profiles of solutions and propagating terrace for a free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity, Equadiff 2019, Leiden, Netherlands.
- 31st, August 2018, Spreading profile of solutions for a free boundary problem of a nonlinear diffusion equation with a positive bistable nonlinearity, Mathematics Seminar, School of Science and Technology, University of New England, Armidale, Australia.
- 8th, July 2018, Spreading and vanishing in a free boundary problem for nonlinear diffusion equations with a given forced moving boundary, 12th AIMS conference on Dynamical Systems, Differential Equations and Applications, National Taiwan University, Taipei, Taiwan
- 7th, July 2018, Spreading profile of solutions for a free boundary problem of a nonlinear diffusion equation with a positive bistable nonlinearity, 12th AIMS conference on Dynamical Systems, Differential Equations and Applications, National Taiwan University, Taipei, Taiwan
- 25th, July 2017, A free boundary problem for nonlinear diffusion equations with a given forced moving boundary, Equadiff 2017, Bratislava, Slovakia
- 2nd, July 2016, Spreading speed and asymptotic profiles of solutions for nonlinear free boundary problems in high space dimension, The 11th AIMS conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, United States
- 1st, July 2016, The Fisher-KPP equation with a moving boundary and a free boundary, The 11th AIMS conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, United States
- 25th, May 2016, The Fisher-KPP equation with a moving boundary and a free boundary, 9th European Conference on Elliptic and Parabolic Equations, Gaeta, Italy
- 8th, March 2016, Spreading speed and profile for free boundary problems of nonlinear diffusion equations, seminar in School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China
- 5th, June 2015, Spreading speeds and profiles of solutions in nonlinear free boundary problems, Asymptotic Problems : Elliptic and Parabolic Issues, A Special Session on Propagation phenomena and free boundary problems, Vilnius, Lithuania.
- 14th, March 2015, Spreading speeds and profiles of solutions in nonlinear free boundary problems, Young Scholars' Workshop on Biomathematics -- Problems, Modeling and Analysis, Tongji University, Shanghai, China.
- 8th July 2014, Spreading speed and sharp asymptotic profiles for solutions in free boundary problems for nonlinear advection-diffusion equations, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain.
- 26th March 2014, Spreading speed and asymptotic profiles for solutions in free boundary problems for nonlinear advection-diffusion equations, PDE Seminar, Tongji University, Shanghai, China.
- 27th August 2013, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, Equadiff 13, Prague, Czech Republic.
- 12th March 2013, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, Mathematics Seminar, School of Science and Technology, University of New England, Armidale, Australia.
- 20th September 2012, Sharp estimate of the spreading speed determined by nonlinear free boundary problems,

Wu Wenjun Key Laboratory of Mathematics, Dynamical Systems Seminar Series No. 15, University of Science and Technology China, Hefei, China. - 4th July 2012, On a dynamics of solution with a transition layer to some bistable reaction diffusion equation, The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orland, United States.
- 25th May 2011, Dynamics of a Front Solution for a Bistable Reaction-diffusion Equation with a Degenerate Spatial Heterogeneity, SIAM Conference on Applications of Dynamical Systems, Snowbird Ski and Summer Resort, Snowbird, Utah, United States.
- 28th May 2010, Dynamics of a front solution for a bistable reaction-diffusion equation with a degenerate spatial heterogeneity, The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden, Germany.
- 23rd July 2009, Dynamics of a transition layer for a scalar bistable reaction-diffusion equation with spatially heterogeneous environments, Equadiff 12, Brno, Czech Republic.
- May 2008, On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous enviromnents. The 7th AIMS Conference on Dynamical Systems and Differential Equations, University of Texas at Arlington, Texas, United States.
- July 2004, Asymptotic profiles of variational solutions of FitzHugh-Nagumo type elliptic system. The Fourth World Congress of Nonlinear Analysts (WCNA-2004), Hyatt Grand Cypress Resort Orlando, Florida, United States.