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arXiv · 1712.06976

Asymptotic stability of the critical Fisher-KPP front using pointwise estimates

Gregory Faye·Matt Holzer
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Abstract

We propose a simple alternative proof of a famous result of Gallay regarding the nonlinear asymptotic stability of the critical front of the Fisher-KPP equation which shows that perturbations of the critical front decay algebraically with rate $t^{-3/2}$ in a weighted $L^\infty$ space. Our proof is based on pointwise semigroup methods and the key remark that the faster algebraic decay rate $t^{-3/2}$ is a consequence of the lack of an embedded zero of the Evans function at the origin for the linearized problem around the critical front.

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Gregory Faye, Matt Holzer. 2017-12-19. Asymptotic stability of the critical Fisher-KPP front using pointwise estimates. https://arxiv.org/abs/1712.06976

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