Speaker： Toshiyuki Ogawa (Meiji University)

Title： Discrete dynamical system approach for bistable reaction-diffusion equations

Time：15:45-16:45, May 5, 2026 (Tuesday)

Venue： Room 440, Astronomy Mathematics Building, National Taiwan University

Abstract：

The behaviors of solutions for bistable reaction-diffusion equations are described by front-type traveling waves. And the existence of traveling waves, the sign of their velocity, and blocking have been extensively studied. Within this context, the influence of domain heterogeneity on the propagation of traveling waves is also actively investigated, mostly through approaches such as comparison theorems and variational methods. If the heterogeneity is periodic, then by viewing the stationary problem as a dynamics with respect to spatial variables, the discrete dynamical system associated with the stationary problem can be naturally defined. The existence of a stationary front solution is equivalent to the existence of a heteroclinic/homoclinic sequence in that discrete dynamical system. In this talk, I will present recent results on the intersection of stable/unstable manifolds associated with stationary problems of the Nagumo equations on infinite intervals with periodic heterogeneity. This talk is based on the joint work with Yoichiro Mori and Chanoknun Sintavanuruk.

Organizer： Chiun-Chuan Chen