Special Session 56: Local and nonlocal diffusion in mathematical biology

Spreading phenomenon in a nonlinear Stefan problem with a certain class of multistable nonlinearity

Hiroshi Matsuzawa
Kanagawa University
Japan
Co-Author(s):    Yuki Kaneko, Yoshio Yamada
Abstract:
In this talk, we discuss a spreading phenomenon described by a nonlinear Stefan problem of a reaction-diffusion equation. In particular, we assume that the reaction term is a positive bistable type nonlinearity class of multi-stable type nonlinearity. We first discuss the classification of asymptotic behaviors of solutions. We next discuss the expanding speeds of the free boundary and the level set of the solution in the spreading case.