Interface dynamics of the porous medium equation with a bistable reaction term

Matthieu Alfaro; Danielle Hilhorst

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arXiv · 1107.3543

Interface dynamics of the porous medium equation with a bistable reaction term

Matthieu Alfaro·Danielle Hilhorst

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Abstract

We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We prove the rapid formation of transition layers which then propagate. We prove the convergence to a sharp interface limit whose normal velocity, at each point, is that of the underlying degenerate travelling wave.

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Matthieu Alfaro, Danielle Hilhorst. 2011-07-18. Interface dynamics of the porous medium equation with a bistable reaction term. https://arxiv.org/abs/1107.3543

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