Wave Solutions to Reaction-Diffusion Systems in Perforated Domains

Travelling waves in periodically perforated domains are shown to exist for large classes of reaction-diffusion systems, provided the homogenized equation admits a nondegenerate travelling wave. This can be applied e.g. to a single equation with bistable nonlinearity and to bistable monotone systems. The proof uses the implicit function theorem of a suitably transformed problem in the space H¹. Furthermore corrector type estimates are given for the wave profile and the wave velocity.