Existence and stability of traveling waves for a nonlocal time-delayed degenerate diffusion equation

This paper is concerned with the existence and stability of traveling wave solutions for a class of non-local time-delayed equations with p-Laplacian diffusion. We first show the existence of traveling wave solutions via monotone iterative method. After providing the existence, uniqueness and regularity of original solution for the Cauchy problem by means of compactness technique, we prove the exponential stability of the non-critical waves. Here the method adapted is the approximated weighted energy method.