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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Faye, Gregory¹  Holzer, Matt² 

[1] Univ Toulouse, Inst Math Toulouse, UPS IMT, UMR 5219, F-31062 Toulouse 9, France

[2] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

关键词: Lotka-Volterra system;    Nonlinear stability;    Pointwise Green?s function;   

DOI  :  10.1016/j.jde.2020.05.012

来源: Elsevier

【 摘 要 】

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-infinity 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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free