Nonplanar traveling fronts for nonlocal dispersal equations with bistable nonlinearity

Abstract

This paper is concerned with nonplanar traveling fronts for a class of nonlocal dispersal equations with bistable nonlinearity. A comparison principle is introduced and employed to establish the existence of traveling fronts with pyramidal shape in $\mathbb R^3$. Although the speed of the pyramidal traveling fronts is not unique, their global average speed is unique. This is possibly the first time that the nonplanar traveling waves for the nonlocal dispersal equations has been studied.