Dynamics for a nonlocal logistic equation with a sedentary compartment and free boundary

This paper investigates a nonlocal logistic equation with a sedentary compartment and free boundary, where population dispersal is modeled using nonlocal diffusion. We first show a spreading-vanishing dichotomy holds. Then by varying the intrinsic rate r of reproduction and diffusion coefficient d respectively, we give detailed criteria for spreading and vanishing, which reveals that the larger r is (or the smaller d is), the more likely spreading is to happen. When spreading occurs, we prove that if and only if a threshold condition is satisfied by kernel function J, there exists a unique finite spreading speed of free boundary which is proved to be the asymptotic spreading speed of density functions u and v. Moreover, we also show that the level sets of u and v have the same spreading speed with free boundaries $g\left(t\right)$ and $h\left(t\right)$.