Existence of traveling wavefronts for a partially non-local diffusion system with degenerate nonlinearities

This paper is concerned with the existence of traveling wavefronts for a class of partially non-local 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 [Formula: see text]. By taking the limit as [Formula: see text] and employing appropriate estimates, we ultimately establish the existence theorem for traveling wavefronts in the class of partially non-local diffusion systems with degenerate nonlinearities. In the end, we demonstrate the applicability of our main theorem by applying it to several biological models.