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arXiv · 1906.07881

Persistence and Extinction of Nonlocal Dispersal Evolution Equations in Moving Habitats

Patrick De Leenheer·Wenxian Shen·Aijun Zhang
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Abstract

This paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed $c$. It is shown that the species becomes extinct if the moving speed $c$ is larger than the so called spreading speed $c^*$, where $c^*$ is determined by the maximum linearized growth rate function. If the moving speed $c$ is smaller than $c^*$, it is shown that the persistence of the species depends on the patch size of the habitat, namely, the species persists if the patch size is greater than some number $L^*$ and in this case, there is a traveling wave solution with speed $c$, and it becomes extinct if the patch size is {smaller} than $L^*$.

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Patrick De Leenheer, Wenxian Shen, Aijun Zhang. 2019-06-19. Persistence and Extinction of Nonlocal Dispersal Evolution Equations in Moving Habitats. https://arxiv.org/abs/1906.07881

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