Regular traveling waves for a reaction-diffusion equation with two nonlocal delays

Abstract

This article concerns regular traveling waves of a reaction-diffusionequation with two nonlocal delays arising from the study of a singlespecies with immature and mature stages and different ages at reproduction. Establishing a necessary condition on the regular traveling waves, we prove the uniqueness of noncritical regular traveling waves,regardless of being monotone or not. Under a quasi-monotone assumption and among other things, we further show that all noncritical monotone traveling waves are exponentially stable, by establishing two comparison theorems and constructing an auxiliary lower equation.