A free boundary problem for spreading under shifting climate

Author(s)
Hu, Yuanyang
Hao, Xinan
Song, Xianfa
Du, Yihong
Publication Date
2020-09-15
Abstract
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed cand obtain a complete classification of the long-time dynamical behaviour of the species. The model is similar to that in with a slight refinement in the free boundary condition. While, like many other works in the literature, investigates the case that unfavourable environment is shifting into the favourable habitat of the concerned species, here we examine the situation that the unfavourable habitat of an invasive species is replaced by a favourable environment with a shifting speed <i>c</i>. We show that a spreading-vanishing dichotomy holds, and there exists a critical speed <i>c</i><sub>0</sub> such that when spreading happens in the case <i>c</i> < <i>c</i><sub>0</sub>, the spreading profile is determined by a semi-wave with forced speed c, but when <i>c</i> &#8925; <i>c</i><sub>0</sub>, the spreading profile is determined by the usual semi-wave with speed <i>c</i><sub>0</sub>.
Citation
Journal of Differential Equations, 269(7), p. 1-20
ISSN
1090-2732
0022-0396
Link
Publisher
Academic Press
Title
A free boundary problem for spreading under shifting climate
Type of document
Journal Article
Entity Type
Publication

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