Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010Reaction-diffusion waves
|Page(s)||1 - 12|
|Published online||27 July 2010|
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
I3M, Université de Montpellier 2, CC051, Place Eugène Bataillon, 34095
Montpellier Cedex 5,
2 CNRS et Laboratoire de Mathématiques, Université de Paris-Sud 11, 91405 Orsay Cedex, France.
* Corresponding author. E-mail:
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.
Mathematics Subject Classification: 35K65 / 35B25 / 35R35 / 92D25.
Key words: degenerate diffusion / singular perturbation / motion by mean curvature / population dynamics
© EDP Sciences, 2010
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