# American Institute of Mathematical Sciences

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doi: 10.3934/dcdsb.2021129
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## A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term

 1 School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China 2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

* Corresponding author: Hongmei Cheng

Received  January 2021 Early access April 2021

Fund Project: The second author is supported by NSFC grant 11701341. The third author is supported by NSFC grant 11771044

This paper is mainly considered a Leslie-Gower predator-prey model with nonlocal diffusion term and a free boundary condition. The model describes the evolution of the two species when they initially occupy the bounded region $[0,h_0]$. We first show that the problem has a unique solution defined for all $t>0$. Then, we establish the long-time dynamical behavior, including Spreading-vanishing dichotomy and Spreading-vanishing criteria.

Citation: Shiwen Niu, Hongmei Cheng, Rong Yuan. A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021129
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