Stability of traveling fronts in a population model with nonlocal delay and advection

Li Liua, Yun-Rui Yanga,* and Shou-Peng Zhanga

Stability of traveling fronts in a population model with nonlocal delay and advection

Authors :

Li Liu^a, Yun-Rui Yang^a,* and Shou-Peng Zhang^a

Author Address :

^aSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu-730070, P.R. China.

*Corresponding author.

Abstract :

In this paper, we are concerned with the stability of traveling fronts in a population model with nonlocal delay and advection under the large initial perturbation (i.e. the initial perturbation around the traveling wave decays exponentially as $x\rightarrow -\infty$, but it can be arbitrarily large in other locations). The globally exponential stability of traveling fronts is established by the weighted-energy method combining with comparison principle, including even the slower waves whose wave speed are close to the critical speed.