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https://hdl.handle.net/1959.11/56207
Title: | Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries |
Contributor(s): | Du, Yihong (author) ; Wu, Chang-Hong (author) |
Publication Date: | 2022-02-03 |
DOI: | 10.1007/s00526-021-02170-8 |
Handle Link: | https://hdl.handle.net/1959.11/56207 |
Abstract: | | In this paper, we revisit the spreading behavior of two invasive species modelled by a diffusion-competition system with two free boundaries in a radially symmetric setting, where the reaction terms depict a weak-strong competition scenario. Our previous work (Du and Wu in Cal Var PDE 57:52, 2018) proves that from certain initial states, the two species develop into a "chase-and-run coexistence" state, namely the front of the weak species v propagates at a fast speed and that of the strong species u propagates at a slow speed, with their population masses largely segregated. Subsequent numerical simulations in Khan et al. (J Math Biol 83:23, 2021) suggest that for all possible initial states, only four different types of long-time dynamical behaviours can be observed: (1) chase-and-run coexistence, (2) vanishing of u with v spreading successfully, (3) vanishing of v with u spreading successfully, and (4) vanishing of both species. In this paper, we rigorously prove that, as the initial states vary, there are exactly five types of long-time dynamical behaviors: apart from the four mentioned above, there exists a fifth case, where both species spread successfully and their spreading fronts are kept within a finite distance to each other all the time. We conjecture that this new case can happen only when a parameter takes an exceptional value, which is why it has eluded the numerical observations of Khan et al. (J Math Biol 83:23, 2021) .
Publication Type: | Journal Article |
Grant Details: | ARC/DP190103757 |
Source of Publication: | Calculus of Variations and Partial Differential Equations, 61(2), p. 1-34 |
Publisher: | Springer |
Place of Publication: | Germany |
ISSN: | 1432-0835 0944-2669 |
Fields of Research (FoR) 2020: | 490410 Partial differential equations 490105 Dynamical systems in applications |
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 |
Publisher/associated links: | https://link.springer.com/article/10.1007/s00526-021-02170-8 |
Appears in Collections: | Journal Article School of Science and Technology
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