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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2022

Asymptotic behavior of nonlocal bistable reaction-diffusion equations

Résumé

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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Dates et versions

hal-03528365 , version 1 (17-01-2022)

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Christophe Besse, Alexandre Capel, Grégory Faye, Guilhem Fouilhé. Asymptotic behavior of nonlocal bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems - Series B, 2022. ⟨hal-03528365⟩
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