Bistable travelling waves for nonlocal reaction diffusion equations
Analysis of PDEs
2013-03-15 v1
Abstract
We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is "above and away", from the intermediate equilibrium. For focusing kernels we prove that, as expected, the wave connects 0 to 1. Our results also apply readily to the nonlocal ignition case.
Cite
@article{arxiv.1303.3554,
title = {Bistable travelling waves for nonlocal reaction diffusion equations},
author = {Matthieu Alfaro and Jerome Coville and Gael Raoul},
journal= {arXiv preprint arXiv:1303.3554},
year = {2013}
}