Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/56290
Title: Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems
Contributor(s): Ai, Shangbing (author); Du, Yihong  (author)orcid ; Jiao, Yujuan (author); Peng, Rui (author)
Publication Date: 2023-05
Early Online Version: 2023-03-28
DOI: 10.1088/1361-6544/acc303
Handle Link: https://hdl.handle.net/1959.11/56290
Abstract: 

In this paper we establish a sharp existence result on weak traveling wave solutions for a general class of multi-species reaction–diffusion systems. Moreover, the minimal speed of the traveling waves is explicitly determined. Such a weak traveling wave solution connects the predator-free equilibrium point E0 at x = −∞ but needs not to connect the coexistence equilibrium E at x = ∞. We apply this result to three important non-cooperative systems: the classical diffusive SIS system for the spread of infectious disease, a predator–prey system with age structure and a generalised Lotka–Volterra predator–prey system of one predator species feeding on n prey species, and prove with the aid of Lyapunov functions and the LaSalle invariance principle that their weak traveling wave solutions are actually traveling wave solutions that connect E at x = ∞. For the SIS system and the generalised Lotka–Volterra predator–prey system, we develop additional techniques to establish the boundedness of their weak traveling wave solutions before applying the LaSalle's invariance principle.

Publication Type: Journal Article
Grant Details: ARC/DP220101820
Source of Publication: Nonlinearity, 36(5), p. 2371-2402
Publisher: Institute of Physics Publishing Ltd
Place of Publication: United Kingdom
ISSN: 1361-6544
0951-7715
Fields of Research (FoR) 2020: 490105 Dynamical systems in applications
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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