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

2019/04/05 by Grégory Faye, Gregory Faye, Faye, Gregory +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP #math.DS

paper · pdf · doi:10.48550/arxiv.1904.03174

arxiv created 2019/04/05 · openalex publication_date 2019/04/05 · arxiv updated 2019/04/08 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

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^∞ 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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