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Existence of planar flame fronts in convective-diffusive periodic media. (English) Zbl 0764.76074
Summary: We prove the existence of planar travelling wave solutions in a reaction diffusion-convection equation with combustion nonlinearity and self- adjoint linear part in \(R^ n\), \(n\geq 1\). The linear part involves diffusion-convection terms and periodic coefficients. These travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media. We use the method of continuation, spectral theory, and the maximum principle. Uniqueness and monotonicity properties of solutions follow from a previous paper [X. Xin, Indiana Univ. Math. J. 40, No. 2, 965-1008 (1991; Zbl 0727.35070)]. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.

MSC:
76V05 Reaction effects in flows
35K57 Reaction-diffusion equations
80A25 Combustion
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