Propagation dynamics in a three-species competition model with nonlocal anisotropic dispersal

Abstract

This paper deals with bistable traveling waves and entire solutions for a three-species competition model with nonlocal anisotropic dispersal. We first establish the existence and monotonicity of traveling waves by the limiting argument on truncation problems. Then using Ikehara’s lemma, we demonstrate the asymptotic behavior of traveling waves, by which the uniqueness of wave profile and wave speed is investigated. Finally, a class of front-like entire solutions are constructed by comparison principle and upper/lower-solutions, and some qualitative properties such as the monotonicity and smoothness of these entire solutions are also obtained.