Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 82, pp. 1-16.

Title: Regular traveling waves for a reaction-diffusion equation with two nonlocal delays
       
Authors: Haiqin Zhao  (Xidian Univ., Xian, Shaanxi, China)
         Shi-Liang Wu (Xidian Univ., Xian, Shaanxi, China)
         
Abstract:  
This article concerns regular traveling waves of a reaction-diffusion
equation with two nonlocal delays arising from the study of a single
species 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.

Submitted August 26, 2022. Published December 12, 2022.
Math Subject Classifications: 35R10, 35B40, 92D30.
Key Words: Regular traveling fronts; reaction-diffusion equation; nonlocal delay; 
           uniqueness; stability