Interface dynamics of the porous medium equation with a bistable reaction term
Analysis of PDEs
2011-07-19 v1
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.
Keywords
Cite
@article{arxiv.1107.3543,
title = {Interface dynamics of the porous medium equation with a bistable reaction term},
author = {Matthieu Alfaro and Danielle Hilhorst},
journal= {arXiv preprint arXiv:1107.3543},
year = {2011}
}