A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term

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 \begin{document}$ [0,h_0] $\end{document} . We first show that the problem has a unique solution defined for all \begin{document}$ t>0 $\end{document} . Then, we establish the long-time dynamical behavior, including Spreading-vanishing dichotomy and Spreading-vanishing criteria.

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