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arXiv · 1303.3554

Bistable travelling waves for nonlocal reaction diffusion equations

Matthieu Alfaro·Jerome Coville·Gael Raoul
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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 $u\equiv 1$ 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.

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Matthieu Alfaro, Jerome Coville, Gael Raoul. 2013-03-14. Bistable travelling waves for nonlocal reaction diffusion equations. https://arxiv.org/abs/1303.3554

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