Stability of Traveling Wave Fronts for Nonlocal Diffusion Equation with Delayed Nonlocal Response

Abstract

In this paper, we consider with the stability of traveling wave fronts for the nonlocal diffusion equation with delay and global response. We first establish the existence and comparison theorem of solutions for the nonlocal reaction-diffusion equation by appealing to the theory of abstract functional differential equation. Then we further show that the traveling wave fronts are asymptotical stability with phase shift. Our main technique is the super and subsolution method coupled with the comparison principle and squeezing method.