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arXiv · 1904.03174

Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model

Gregory Faye·Matt Holzer
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Abstract

We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front decay algebraically with rate $t^{-3/2}$ in a weighted $L^\infty$ space. Our proof relies on pointwise semigroup methods and utilizes in a crucial way that the faster 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. 2019-04-05. Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model. https://arxiv.org/abs/1904.03174

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