Asymptotic behavior of nonlocal bistable reaction-diffusion equations
Analysis of PDEs
2022-01-19 v1
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.
Cite
@article{arxiv.2201.06482,
title = {Asymptotic behavior of nonlocal bistable reaction-diffusion equations},
author = {Christophe Besse and Alexandre Capel and Grégory Faye and Guilhem Fouilhé},
journal= {arXiv preprint arXiv:2201.06482},
year = {2022}
}