Nonlinear Stability of Traveling Wavefronts for Delayed Reaction-diffusion Equation with Nonlocal Diffusion

Abstract

In this paper, we consider a class of nonlocal dispersal equation with nonlocal time-delayed reaction. We prove that all noncritical wavefronts are globally exponentially stable by the weighted energy method and comparison principle. However, for the critical wavefronts, we prove that they are globally asymptotically stable.