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arXiv · 2201.06482

Asymptotic behavior of nonlocal bistable reaction-diffusion equations

Christophe Besse·Alexandre Capel·Grégory Faye·Guilhem Fouilhé
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Abstract

In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction kernel and the diffusion coefficient, we show that the solutions can either: propagate, go extinct or remain pinned. We especially focus on the latter regime where solutions are pinned by thoroughly studying discontinuous ground state solutions of the problem for a specific interaction kernel serving as a case study. We also present a detailed numerical analysis of the problem.

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Christophe Besse, Alexandre Capel, Grégory Faye, Guilhem Fouilhé. 2022-01-17. Asymptotic behavior of nonlocal bistable reaction-diffusion equations. https://arxiv.org/abs/2201.06482

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