| Abstract: |
| We revisit the stability of the critical front in the Fisher-KPP equation, which travels with the linear spreading speed $c = 2$. We recover a celebrated result of Gallay with a new method, establishing stability of the critical front with optimal decay rate $t^{-3/2}$ as well as an asymptotic description of the perturbation of the front. Our approach is based on studying detailed regularity properties of the resolvent for this problem in algebraically weighted spaces near the branch point in the absolute spectrum, and renders the nonlinear analysis much simpler. We further explore the relationship between the localization of perturbations and their decay rate. |
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