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Generation of Interface for an Allen-Cahn Equation withNonlinear Diffusion

Published online by Cambridge University Press:  27 July 2010

M. Alfaro  and
D. Hilhorst
M. Alfaro
Affiliation:
I3M, Université de Montpellier 2, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.
D. Hilhorst*
Affiliation:
CNRS et Laboratoire de Mathématiques, Université de Paris-Sud 11, 91405 Orsay Cedex, France.
*
* Corresponding author. E-mail:danielle.hilhorst@math.u-psud.fr
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Abstract

In this note, we consider a nonlinear diffusion equation with a bistable reaction termarising in population dynamics. Given a rather general initial data, we investigate itsbehavior for small times as the reaction coefficient tends to infinity: we prove ageneration of interface property.

Keywords

degenerate diffusionsingular perturbationmotion by mean curvaturepopulation dynamics
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 1 - 12
Copyright
© EDP Sciences, 2010

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