Talk

Wave Solutions to Reaction-Diffusion Systems in Perforated Domains

  • Steffen Heinze (MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)

Abstract

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.

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