Affiliations: I3M, Université de Montpellier 2, Montpellier Cedex, France. E-mail: malfaro@math.univ-montp2.fr | CNRS and Laboratoire de Mathématiques, Université de Paris-Sud 11, Orsay Cedex, France. E-mail: danielle.hilhorst@math.u-psud.fr
Note: [] Corresponding author: Matthieu Alfaro, I3M, Université de Montpellier 2, CC051, Place Eugène Bataillon, 34095 Mont- pellier Cedex 5, France. E-mail: malfaro@math.univ-montp2.fr.
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: degenerate diffusion, singular perturbation, sharp interface limit, population dynamics
