# American Institute of Mathematical Sciences

May  2014, 19(3): 801-815. doi: 10.3934/dcdsb.2014.19.801

## Exponential stability of the traveling fronts for a viscous Fisher-KPP equation

 1 Center for PDE, East China Normal University, Shanghai, 200241, China, China 2 School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

Received  July 2013 Revised  November 2013 Published  February 2014

This paper is concerned with the stability of traveling front solutions for a viscous Fisher-KPP equation. By applying geometric singular perturbation method, special Evans function estimates, detailed spectral analysis and $C_0$ semigroup theories, each traveling front solution with wave speed $c<-2\sqrt{f^\prime(0)}$ is proved to be locally exponentially stable in some appropriate exponentially weighted spaces.
Citation: Lina Wang, Xueli Bai, Yang Cao. Exponential stability of the traveling fronts for a viscous Fisher-KPP equation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 801-815. doi: 10.3934/dcdsb.2014.19.801
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