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https://hdl.handle.net/1959.11/31814
Title: | A Climate Shift Model with Free Boundary: Enhanced Invasion | Contributor(s): | Du, Yihong (author) ; Hu, Yuanyang (author); Liang, Xing (author) | Publication Date: | 2023-03 | Early Online Version: | 2021-06-25 | DOI: | 10.1007/s10884-021-10031-3 | Handle Link: | https://hdl.handle.net/1959.11/31814 | Abstract: | We examine how climate change enhances the spreading of an invading species through a nonlinear diffusion equation of the form ut = duxx+A (x − ct) u−bu2 with a free boundary, where climate change causes more favourable environment shifting into the habitat of the species with a constant speed c > 0. The free boundary represents the invading front of the expanding population range. We show that the long-time dynamics of this model obeys a spreading-vanishing dichotomy, which is best illustrated by using a suitably parameterised family of initial functions u0σ increasing continuously in σ: there exists a critical value σ∗ ∈ (0,∞) so that the species vanishes ultimately when σ ∈ (0, σ∗], and it spreads successfully when σ > σ∗ . However, when spreading is successful, there exist two threshold speeds c0 < c1 that divide the spreading profile into strikingly different patterns. For example, when c < c0 the profile of the population density function u(t, x) approaches a propagating pair composed of a traveling wave with speed c and a semi-wave with speed c0; when c0 < c < c1, it approaches a semi-wave with speed c, and when c > c1, it approaches a semi-wave with speed c1. | Publication Type: | Journal Article | Source of Publication: | Journal of Dynamics and Differential Equations, 35(1), p. 771-809 | Publisher: | Springer New York LLC | Place of Publication: | United States of America | ISSN: | 1572-9222 1040-7294 |
Fields of Research (FoR) 2020: | 490410 Partial differential equations 490102 Biological mathematics |
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 |
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Appears in Collections: | Journal Article School of Science and Technology |
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