A verified computation of steady-state solutions to Reaction-Diffusion equations

摘要

This talk is concerned with a numerical verification method of steady-state solutions to Reaction-Diffusion equations with the Dirichlet boundary problem. Solutions of Reaction-Diffusion equations are applied to understand various phenomena in biology, chemistry and so on. A numerical verification of FitzHugh-Nagumo model has studied by Y. Watanabe using Nakao's theory. Watanabe's method treat bounded convex domains. Our method is based on Newton-Kantorovich's theorem for the direct product space H_0~1(Ω)×H_0~1(Ω). Some numerical examples are presented on bounded convex and non-convex domains.