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Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity. (English) Zbl 0769.35033
Summary: We prove the existence of multidimensional traveling wave solutions of the bistable reaction-diffusion equation with periodic coefficients under the condition that these coefficients are close to constants. In the case of one space dimension, we prove their asymptotic stability.

MSC:
35K57 Reaction-diffusion equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B35 Stability in context of PDEs
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