Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment

Weiyi Zhang; Zuhan Liu; Ling Zhou

doi:10.3934/dcdsb.2020256

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2021, Volume 26, Issue 7: 3767-3784. Doi: 10.3934/dcdsb.2020256

This issue Previous Article The coupled 1:2 resonance in a symmetric case and parametric amplification model Next Article Evolutionary de Rham-Hodge method

Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment

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

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

Received: December 31, 2019

Revised: June 30, 2020

Early access: August 2020

Published: July 2021

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Abstract

In this paper we study a nonlocal diffusion model with double free boundaries in time periodic environment, which is the natural extension of the free boundary model in [17], where local diffusion is used to describe the population dispersal. We give the existence and uniqueness of global solution and consider the properties of principle eigenvalue of time-periodic parabolic-type eigenvalue problem. With the help of attractivity of time periodic solutions, we establish a spreading-vanishing dichotomy. The sharp criteria for spreading and vanishing are also obtained.

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

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