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

• * Corresponding author: Ling Zhou
• 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.

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

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