On uniqueness of traveling waves for a reaction diffusion equation with spatio-temporal delay

Abstract

This paper is devoted to study the uniqueness (up to translation) of traveling wave solutions for a general reaction-diffusion equation with spatio-temporal delay . It is shown that the traveling wave solutions with any given admissible speed (including the minimal wave speed ) of this general equation are unique up to translation under certain assumptions. The main result helps us to solve some open problems on the uniqueness of traveling wave solutions of a few well-known models such as the diffusive Nicholson's blowflies model, the diffusive Mackey-Glass' hematopoiesis model, an age-structured population model, an epidemic model and a reaction-diffusion model with a quiescent stage.