A singular perturbation problem for a scalar bistable nonlocal reaction-diffusion equation is treated. It is rigorously proved that the layer solutions of this nonlocal reaction-diffusion equation converge to solutions of the averaged mean curvature flow on a finite time interval as the singular perturbation parameter tends to zero.
Publié le : 2008-07-15
Classification:
Singular perturbation,
bistable nonlocal reaction-diffusion equation,
internal transition layer,
interface,
the averaged mean curvature flow,
35B25,
35K57
@article{1220619461,
author = {Okada, Koji},
title = {Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow},
journal = {Hiroshima Math. J.},
volume = {38},
number = {1},
year = {2008},
pages = { 263-313},
language = {en},
url = {http://dml.mathdoc.fr/item/1220619461}
}
Okada, Koji. Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow. Hiroshima Math. J., Tome 38 (2008) no. 1, pp. 263-313. http://gdmltest.u-ga.fr/item/1220619461/