Approximation of nonlocal dispersal problem with inhomogeneous kernel

In this paper, we study the Neumann problem for a class of nonlocal dispersal models with inhomogeneous kernel function. We investigate the existence, uniqueness, and limit of solutions when the inhomogeneous diffusion kernel is rescaled. Our result exhibits that the inhomogeneous nonlocal dispersal equation is analogous to local problem without convection in the limit case.