Abstract
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≧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. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.
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Communicated by P. H. Rabinowitz
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Xin, J.X. Existence of planar flame fronts in convective-diffusive periodic media. Arch. Rational Mech. Anal. 121, 205–233 (1992). https://doi.org/10.1007/BF00410613
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DOI: https://doi.org/10.1007/BF00410613