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arXiv · 1201.4920

Traveling Wave Solutions of Advection-Diffusion Equations with Nonlinear Diffusion

Léonard Monsaingeon·Alexeï Novikov·Jean-Michel Roquejoffre
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Abstract

We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*, +{\infty}, where c* > 0 is explicitly computed but may not be optimal. We also prove that a free boundary hy- persurface separates a region where u = 0 and a region where u > 0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u > 0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.

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Léonard Monsaingeon, Alexeï Novikov, Jean-Michel Roquejoffre. 2012-01-24. Traveling Wave Solutions of Advection-Diffusion Equations with Nonlinear Diffusion. https://doi.org/10.1016/j.anihpc.2012.11.003

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