A numerical verification method using H_σ~1-norm for an elliptic system of FitzHugh-Nagumo type

摘要

This talk is concerned with a numerical verification method of an elliptic system of FitzHugh-Nagumo type with the Dirichlet boundary problem. G. Sweers and W. C. Troy have studied from theoretical and numerical side on the bifurcation curve for this system in both one and two dimensions. A numerical verification theory for this system has been proposed by Y. Watanabe using Nakao's theory. In this talk, we present another verification method using (H_σ)~1 -norm. The aim of our method is that (H_σ)~1-norm yields better estimates than usual (H_σ)~1-norm when a given parameter ε is small.