Generation of interface for an Allen-Cahn equation with nonlinear diffusion

Matthieu Alfaro (1) , Danielle Hilhorst (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Danielle Hilhorst. Generation of interface for an Allen-Cahn equation with nonlinear diffusion. Mathematical Modelling of Natural Phenomena, 2010, 5 (5), pp.1--12. ⟨10.1051/mmnp/20105501⟩. ⟨hal-00417485⟩