| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010
Reaction-diffusion waves
|
|
|---|---|---|
| Page(s) | 1 - 12 | |
| DOI | https://doi.org/10.1051/mmnp/20105501 | |
| Published online | 27 July 2010 | |
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
1
I3M, Université de Montpellier 2, CC051, Place Eugène Bataillon, 34095
Montpellier Cedex 5,
France.
2
CNRS et Laboratoire de Mathématiques, Université de Paris-Sud
11, 91405
Orsay Cedex,
France.
* Corresponding author. E-mail:
danielle.hilhorst@math.u-psud.fr
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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