Abstract
We compute the effective wavefront speeds of reaction-diffusion equations in periodically layered media with coefficients that have small-amplitude oscillations around a uniform mean state. We compare them with the corresponding wavefront speeds in the uniform state. We analyze a one-dimensional model where wave propagation is along the layering direction of the medium and a two-dimensional shear flow model where wave propagation is othogonal to the layering direction. We find that the effective wave speed is smaller in the one-dimensional model and is larger in the two-dimensional model for both bistable cubic and quadratic nonlinearities of the Kolmogorov-Petrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.
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Dedicated to Jerry Percus on the occasion of his 65th birthday.
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Papanicolaou, G., Xin, X. Reaction-diffusion fronts in periodically layered media. J Stat Phys 63, 915–931 (1991). https://doi.org/10.1007/BF01029991
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DOI: https://doi.org/10.1007/BF01029991