| Author(s) |
Du, Yihong
Hu, Yuanyang
Liang, Xing
|
| Publication Date |
2023-03
|
| Abstract |
We examine how climate change enhances the spreading of an invading species through a nonlinear diffusion equation of the form <i>u<sub>t</sub></i> = <i>du<sub>xx</sub></i>+A (<i>x</i> − <i>ct</i>) <i>u</i>−<i>bu</i><sup>2</sup> with a free boundary, where climate change causes more favourable environment shifting into the habitat of the species with a constant speed <i>c</i> > 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 <i>u</i><sub>0</sub><sup>σ</sup> increasing continuously in <i>σ</i>: there exists a critical value <i>σ</i><sub>∗</sub> ∈ (0,∞) so that the species vanishes ultimately when <i>σ</i> ∈ (0, <i>σ</i><sub>∗</sub>], and it spreads successfully when <i>σ</i> > <i>σ</i><sup>∗</sup> . However, when spreading is successful, there exist two threshold speeds <i>c</i><sub>0</sub> < <i>c</i><sub>1</sub> that divide the spreading profile into strikingly different patterns. For example, when <i>c</i> < <i>c</i><sub>0</sub> the profile of the population density function <i>u</i>(t, x) approaches a propagating pair composed of a traveling wave with speed <i>c</i> and a semi-wave with speed <i>c</i><sub>0</sub>; when <i>c</i><sub>0</sub> < <i>c</i> < <i>c</i><sub>1</sub>, it approaches a semi-wave with speed <i>c</i>, and when <i>c</i> > <i>c</i><sub>1</sub>, it approaches a semi-wave with speed <i>c</i><sub>1</sub>.
|
| Citation |
Journal of Dynamics and Differential Equations, 35(1), p. 771-809
|
| ISSN |
1572-9222
1040-7294
|
| Link | |
| Publisher |
Springer New York LLC
|
| Title |
A Climate Shift Model with Free Boundary: Enhanced Invasion
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| Type of document |
Journal Article
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| Entity Type |
Publication
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