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arXiv · 1011.4561

Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation

Gregoire Nadin·Benoit Perthame·Min Tang
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Abstract

This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in \cite{BNPR} but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states $0$ and $1$, which is a striking fact since $0$ is dynamically unstable and $1$ is unstable in the sense of Turing.

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Gregoire Nadin, Benoit Perthame, Min Tang. 2010-11-20. Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation. https://arxiv.org/abs/1011.4561

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