# American Institute of Mathematical Sciences

July  2020, 19(7): 3651-3672. doi: 10.3934/cpaa.2020161

## The dynamics of nonlocal diffusion systems with different free boundaries

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

* Corresponding author

Received  July 2019 Revised  January 2020 Published  April 2020

Fund Project: The third author is supported by NSFC grants 11771110, 11971128

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.

Citation: Lei Li, Jianping Wang, Mingxin Wang. The dynamics of nonlocal diffusion systems with different free boundaries. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3651-3672. doi: 10.3934/cpaa.2020161
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