Existence and stability of invasion traveling waves for a competition system with random vs. nonlocal dispersals

The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs. nonlocal dispersal. We first prove the existence of invasion traveling waves via using the theory of asymptotic speeds of spread. Then we prove the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces by using the weighted energy and the squeezing technique.