Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/31893
Title: Semi-wave and spreading speed of the nonlocal Fisher-KPP equation with free boundaries
Contributor(s): Du, Yihong  (author)orcid ; Li, Fang (author); Zhou, Maolin  (author)
Publication Date: 2021-10
Early Online Version: 2021-08-16
DOI: 10.1016/j.matpur.2021.08.008
Handle Link: https://hdl.handle.net/1959.11/31893
Abstract: 

In Cao, Du, Li and Li [9], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [18] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to follow a spreading-vanishing dichotomy. However, when spreading happens, the question of spreading speed was left open in [9]. In this paper we obtain a rather complete answer to this question. We find a threshold condition on the kernel function such that spreading grows linearly in time exactly when this condition holds, which is achieved by completely solving the associated semi-wave problem that determines this linear speed; when the kernel function violates this condition, we show that accelerated spreading happens.

Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: Journal de Mathematiques Pures et Appliquees, v.154, p. 30-66
Publisher: Elsevier Masson
Place of Publication: France
ISSN: 1776-3371
0021-7824
Fields of Research (FoR) 2020: 490410 Partial differential equations
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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