Global asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundaries

Weiyi Zhang; Ling Zhou

doi:10.3934/dcdsb.2022062

Article Contents

2022, Volume 27, Issue 12: 7745-7782. Doi: 10.3934/dcdsb.2022062

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Global asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundaries

Weiyi Zhang and
Ling Zhou^,

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

^*Corresponding author: Ling Zhou
^*Corresponding author: Ling Zhou

Received: April 30, 2021

Early access: March 2022

Published: December 2022

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Abstract

In this paper we give a classification of the global asymptotic stability for a nonlocal diffusion competition model with free boundaries consisting of an invasive species with density $ u $ and a native species with density $ v $. We not only prove that such nonlocal diffusion problem has a unique global solution and also determine the long-time asymptotic behavior of the solution for three competition cases : (I) $ u $ is an inferior competitor, (II) $ u $ is a superior competitor and (III) the weak competition case. Especially, in case (II), under some additional conditions, we determine the long-time asymptotic behavior of the solution when vanishing happens. Moreover, the criteria for spreading and vanishing are obtained.

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Mathematics Subject Classification: 35K51, 35R35, 92B05, 35B40.

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