Convergence to a Single Wave in the Fisher-KPP Equation(Dedicated to Haim Brezis,with admiration and respect)

James NOLEN; Jean-Michel ROQUEJOFFRE; Lenya RYZHIK

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Convergence to a Single Wave in the Fisher-KPP Equation(Dedicated to Haim Brezis,with admiration and respect)

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The authors study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame moving as 2t-(3/2 )log t+x∞, the solution of the equation converges as t → +∞ to a translate of the traveling wave corresponding to the minimal speed c_* = 2. The constant x∞ depends on the initial condition u(0, x). The proof is elaborate, and based on probabilistic arguments.The purpose of this paper is to provide a simple proof based on PDE arguments.

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《数学年刊B辑（英文版）》 |2017年第2期|629-646|共18页
作者
James NOLEN; Jean-Michel ROQUEJOFFRE; Lenya RYZHIK;
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作者单位

Department of Mathematics;

Duke University;

Durham;

NC 27708;

USA;

Institut de Mathématiques(UMR CNRS 5219);

Université Paul Sabatier;

118 route de Narbonne;

31062 Toulouse cedex;

Fraxlce;

Department of Mathematics;

Stanford University;

Stanford CA;

94305;

USA.;

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原文格式 PDF
正文语种 chi
中图分类微分方程、积分方程;
关键词
Traveling; waves; KPP; Front; propagation; Asymptotic; analysis; Reaction-diffusion;

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Convergence to a Single Wave in the Fisher-KPP Equation(Dedicated to Haim Brezis,with admiration and respect)

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