The effect of an unfavorable region on the invasion process of a species

Pengchao Lai; Junfan Lu

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arXiv · 2301.11493

The effect of an unfavorable region on the invasion process of a species

Pengchao Lai·Junfan Lu

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Abstract

To model a propagating phenomena through the environment with an unfavorable region, we consider a reaction diffusion equation with negative growth rate in the unfavorable region and bistable reaction outside of it. We study rigorously the influence of $L$, the width of the unfavorable region, on the propagation of solutions. It turns out that there exists a critical value $L^*$ depending only on the reaction term such that, when $L L^*$ we have a trichotomy result: spreading/residue happens for a species with large/small initial population, but, for a species with medium-sized initial data, it can not pass through the region either and converges to a transition steady state.

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Pengchao Lai, Junfan Lu. 2023-01-27. The effect of an unfavorable region on the invasion process of a species. https://arxiv.org/abs/2301.11493

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