Bistable Wave Fronts in a Stage-Structured Reaction-Diffusion Model for a Single Species with Distributed Maturation Delay

This paper is concerned with bistable wave fronts in a class of nonlocal reaction diffusion model for a single species with stage structure and distributed maturation delay. By choosing the strong and weak kernel functions to transform system with delays to a two- or three-dimensional system without any delays, the existence of traveling wave fronts is established by abstract results. Then we prove the asymptotic stability (up to translation) of bistable wave fronts and the uniqueness of wave speeds by spectral analysis and upper and lower solution technique, respectively. At last, we apply these results to a single species model with special nonlinearity.