Wave Solutions to Reaction-Diffusion Systems in Perforated Domains

Abstract

Traveling waves in periodically perforated domains are shown to exist for large classes of reaction-diffusion systems, provided the homogenized equation admits a non-degenerate traveling wave. This can be applied e.g. to a single equation with bistable non-linearity and to bistable monotone systems. The proof uses the implicit function theorem of a suitably transformed problem in the space $H^1$. Furthermore, corrector-type estimates are given for the wave profile and the wave velocity.