Existence of Traveling Wavefronts for a Partially Nonlocal Diffusion System with Degenerate Nonlinearities

This paper is concerned with the existence of traveling wavefronts for a class of partially nonlocal diffusion system with degenerate nonlinearities. We first introduce two fundamental lemmas: a strong maximum principle and an existence theorem for certain integro-differential systems. Building on these lemmas, we then prove the existence of solutions to an auxiliary problem. With the auxiliary results in hand, we proceed to construct a positive and increasing solution to a perturbation problem for any ϵ > 0. By taking the limit as ϵ → 0 and employing appropriate estimates, we ultimately establish the existence theorem for traveling wavefronts in the class of partially nonlocal diffusion systems with degenerate nonlinearities. In the end, we demonstrate the applicability of our main theorem by applying it to several biological models.