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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 3, 2001, pp. 661–676
DOI: 10.4171/ZAA/1037

Published online: 2001-09-30

Wave Solutions to Reaction-Diffusion Systems in Perforated Domains

S. Heinze[1]

(1) Mathematik in den Naturwissenschaften, Leipzig, Germany

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.

Keywords: Reaction-Diffusion equations, front propagation, homogenization

Heinze S.: Wave Solutions to Reaction-Diffusion Systems in Perforated Domains. Z. Anal. Anwend. 20 (2001), 661-676. doi: 10.4171/ZAA/1037