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 . Furthermore, corrector-type estimates are given for the wave profile and the wave velocity.
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S. Heinze, Wave Solutions to Reaction-Diffusion Systems in Perforated Domains. Z. Anal. Anwend. 20 (2001), no. 3, pp. 661–676DOI 10.4171/ZAA/1037