Abstract
This paper is concerned with the stability of traveling frontsolutions for a viscous Fisher-KPP equation. By applying geometricsingular perturbation method, special Evans function estimates,detailed spectral analysis and $C_0$ semigroup theories, eachtraveling front solution with wave speed $c<-2\sqrt{f^\prime(0)}$ isproved to be locally exponentially stable in some appropriateexponentially weighted spaces.
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