| Author(s) |
Hu, Yuanyang
Hao, Xinan
Du, Yihong
|
| Publication Date |
2021-12
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| Abstract |
<p>In this paper, we consider a free boundary model in one space dimension which describes the spreading of a species subject to climate change, where favorable environment is shifting away with a constant speed c > 0 and replaced by a deteriorated yet still favorable environment. We obtain two threshold speeds c<sub>1</sub> < c<sub>0</sub> and a complete classification of the long-time dynamics of the model, which reveals significant differences between the cases 0 < c < c<sub>1</sub>, c = c<sub>1</sub>, c<sub>1</sub> < c < c<sub>0</sub> and c ≥ c<sub>0</sub>. For example, when c<sub>1</sub> < c < c<sub>0</sub>, for a suitably parameterized family of initial functions <i>u</i>σ0 increasing continuously in σ, we show that there exists 0 < σ<sub>⁎</sub> < σ<sup>⁎</sup> < ∞ such that the species vanishes eventually when σ ∈ (0, σ<sub>⁎</sub>], it spreads with asymptotic speed c<sub>1</sub> when σ ∈ (σ<sub>⁎</sub>, σ<sup>⁎</sup>), it spreads with forced speed c when σ = σ<sup>⁎</sup>, and it spreads with speed c<sub>0</sub> when σ > σ<sup>⁎</sup>. Moreover, in the last case, while the spreading front propagates with asymptotic speed c<sub>0</sub>, the profile of the population density function <i>u</i>(<i>t, x</i>) approaches a propagating pair consisting of a traveling wave with speed c and a semi-wave with speed c<sub>0</sub>.</p>
|
| Citation |
Communications in Contemporary Mathematics, 23(8), p. 1-49
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| ISSN |
1793-6683
0219-1997
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| Link | |
| Publisher |
World Scientific Publishing Co Pte Ltd
|
| Title |
Spreading under shifting climate by a free boundary model: Invasion of deteriorated environment
|
| Type of document |
Journal Article
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| Entity Type |
Publication
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