Invasion traveling wave solutions of a predator-prey model with nonlocal dispersal

Abstract

This paper is concerned with the existence of traveling wave solutions for a predator-prey model with nonlocal dispersal. By applying Schauder’s fixed point theorem and a cross-iteration technique, we reduce the existence of traveling wave solutions to the existence of a pair of super-sub solutions. More precisely, we proved that there exists a positive constant c* such that when c > c*, the nonlocal dispersal predator-prey system admits a traveling wave solution. In particular, the existence of traveling wave solution for c=c* is also established by asymptotic spreading theory and comparison principle. Furthermore, by investigating the non-existence of traveling wave solution, we determine the minimal speed of traveling wave solution for this model. This provides an estimation of the invasion speed. The novelty of this work lies in the construction of super-sub solutions and the proof of the complete continuity of operator.