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arXiv · 1801.05653

On the stability of the state 1 in the non-local Fisher-KPP equation in bounded domains

Camille Pouchol
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Abstract

We consider the non-local Fisher-KPP equation on a bounded domain with Neu-mann boundary conditions. Thanks to a Lyapunov function, we prove that under a general hypothesis on the Kernel involved in the non-local term, the homogenous steady state 1 is globally asymptotically stable. This assumption happens to be linked to some conditions given in the literature, which ensure that travelling waves link 0 to 1.

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Camille Pouchol. 2018-01-17. On the stability of the state 1 in the non-local Fisher-KPP equation in bounded domains. https://arxiv.org/abs/1801.05653

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