Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/31814
Title: A Climate Shift Model with Free Boundary: Enhanced Invasion
Contributor(s): Du, Yihong  (author)orcid ; 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 (xct) ubu2 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
Appears in Collections:Journal Article
School of Science and Technology

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