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Generation of interface for an Allen-Cahn equation with nonlinear diffusion
Journal article   Open access   Peer reviewed

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

Matthieu Alfaro and Danielle Hilhorst
Mathematical Modelling of Natural Phenomena, Vol.5(5), pp.1--12.
2010

Abstract

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.
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