Two species nonlocal diffusion systems with free boundaries

Title
Two species nonlocal diffusion systems with free boundaries
Publication Date
2022-03
Author(s)
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Wang, Mingxin
Zhao, Meng
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
AIMS Press
Place of publication
United States of America
DOI
10.3934/dcds.2021149
UNE publication id
une:1959.11/31904
Abstract

We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here the population dispersal is described by "nonlocal diffusion" instead of "local diffusion". We prove that such a nonlocal diffusion problem with free boundary has a unique global solution, and for models with Lotka-Volterra type competition or predator-prey growth terms, we show that a spreading-vanishing dichotomy holds, and obtain criteria for spreading and vanishing; moreover, for the weak competition case and for the weak predation case, we can determine the long-time asymptotic limit of the solution when spreading happens. Compared with the single species free boundary model with nonlocal diffusion considered recently in [7], and the two species cases with local diffusion extensively studied in the literature, the situation considered in this paper involves several new difficulties, which are overcome by the use of some new techniques.

Link
Citation
Discrete and Continuous Dynamical Systems. Series A, 42(3), p. 1127-1162
ISSN
1553-5231
1078-0947
Start page
1127
End page
1162

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