Asymptotic Stability and Uniqueness of Critical Traveling Waves in a Reaction-Diffusion Model With Nonlocal Delay

We study the stability and uniqueness of critical traveling waves for nonlocal delayed reaction-diffusion model for a single species with age structure. By introducing a suitable solution space, using the anti-weighted energy method and the nonlinear Halanay's inequality, we prove the exponential stability of critical traveling waves when the initial perturbations are suitably small in a weighted norm. As a corollary of stability result, we obtain the uniqueness of critical traveling waves up to translations. Meanwhile, we apply our result to the nonlocal delayed diffusive Nicholson's blowflies equation in population dynamics. Our results provide significant insight into theoretical research and practical application since the spreading speeds of the traveling waves in the applications of biological sciences usually are the critical speed.