Year: 2022
Author: He Zhang, Yong Li, Xue Yang
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 389–421
Abstract
We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and compactly supported initial data. We show that for small values of the parameter the corresponding solutions decay to 0, while for large values the related solutions converge to 1 uniformly on compacts. Moreover, we prove that the transition from extinction (converging to 0) to propagation (converging to 1) is sharp. Numerical results are provided to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0003
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 389–421
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Nonlocal reaction diffusion equation asymptotic behaviors threshold solution sharp transition.
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