Front propagation in reaction-diffusion equations and the domain geometry
演讲者
俣野 博
时间
2025年03月19日 17:00 至 18:00
地点
A6-101
线上
Zoom 388 528 9728
(BIMSA)
摘要
In recent years, the behavior of solution fronts of reaction-diffusion equations in the presence of obstacles has attracted much attention among many researchers. In general, the behavior of the fronts is under a strong influence of the curvature effects, therefore their interaction with the obstacles can be highly complex.
In this talk, I will first consider curvature-dependent motion of plane curves in an infinite strip whose boundaries have a bumpy shape and discuss the influence of the boundary shape on the speed of propagation of the curve. Such a motion of plane curves appears in the singular limit of a certain reaction-diffusion equations. I will also talk about the homogenization limit of the problem when the boundary bumps become finer and finer. This part of the talk is based partly on my old joint work with Bendong Lou and Ken-ichi Nakamura and partly on my recent joint work with Ryunosuke Mori.
In the second part of my talk, I will consider solution fronts of a reaction-diffusion equation in the presence of a wall with many holes, and discuss whether the front can pass through the wall and continues to propagate toward the other side of the wall (“propagation”) or is blocked by the wall (“blocking”). This problem has led to a variety of interesting mathematical questions that are far richer than we had originally anticipated. Many questions still remain open. This part of the talk is joint work with Henri Berestycki and Francois Hamel.
演讲者介绍
Hiroshi Matano is currently Distinguished Professor Emeritus at Meiji University, Japan, and was the director of Meiji Institute for Advanced Study of Mathematical Sciences (MIMS) from 2019 to 2023. He is also Professor Emeritus at the University of Tokyo. He obtained DSc degree from Kyoto University in 1982. He was awarded Spring Prize in 1990, which is the most prestigious prize of the Mathematical Society of Japan, and was a 45-minute invited speaker at ICM 94, Zurich. He was also a distinguished Ordway Visiting Professor at University of Minnesota in 1990 and 2018.
His research interests include qualitative theory of nonlinear parabolic equations and elliptic equations such as stability, long-time behavior and formation of singularities. Among other things, he has made fundamental contributions to the qualitative theory of one-dimensional nonlinear parabolic equations by introducing a new analytical tool based on the zero-number principle, which has since then become a common technique among many researchers. He is also among the early pioneers in developing the theory of order-preserving dynamical systems and its applications, and in exploring the relation between the stability of solutions and the domain geometry.
His research interests include qualitative theory of nonlinear parabolic equations and elliptic equations such as stability, long-time behavior and formation of singularities. Among other things, he has made fundamental contributions to the qualitative theory of one-dimensional nonlinear parabolic equations by introducing a new analytical tool based on the zero-number principle, which has since then become a common technique among many researchers. He is also among the early pioneers in developing the theory of order-preserving dynamical systems and its applications, and in exploring the relation between the stability of solutions and the domain geometry.