The dynamics of nonlocal diffusion systems with different free boundaries

Lei Li; Jianping Wang; Mingxin Wang

doi:10.3934/cpaa.2020161

Article Contents

2020, Volume 19, Issue 7: 3651-3672. Doi: 10.3934/cpaa.2020161

This issue Previous Article The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity Next Article Improved Sobolev inequalities and critical problems

The dynamics of nonlocal diffusion systems with different free boundaries

School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

^* Corresponding author
^* Corresponding author

Received: June 30, 2019

Revised: December 31, 2019

Published: April 2020

The third author is supported by NSFC grants 11771110, 11971128

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Abstract

This paper is concerned with a class of free boundary models with "nonlocal diffusions'' and different free boundaries, which are natural extensions of free boundary problems of reaction diffusion systems with different free boundaries in [M.X.Wang and Y.Zhang, J. Differ. Equ., 264 (2018), 3527-3558] and references therein. These different free boundaries, which may intersect each other as time evolves, are used to describe the spreading front of the species. We prove that such kind of nonlocal diffusion problems has a unique global solution. Moreover, we investigate the long time behavior of global solution and criteria of spreading and vanishing for the classical Lotka-Volterra competition, prey-predator and mutualist models.

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Mathematics Subject Classification: Primary: 35K57, 35R20, 35R35, 92D25.

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