Dynamics of interfaces in the Fisher-KPP equation for slowly decaying initial data

被引：1

作者：

Ninomiya, Hirokazu ^{[1
]}

Yanagida, Eiji ^{[2
]}

机构：

[1] Meiji Univ, Sch Interdisciplinary Math Sci, Nakano Ku, Tokyo 1648525, Japan

[2] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 08期

关键词：

Fisher-KPP equation; Hamilton-Jacobi equation; Dynamics of interfaces; FRONT PROPAGATION; UNSTABLE STATES; CONVERGENCE; DIFFUSION; STABILITY; BEHAVIOR; VELOCITY;

D O I：

10.1016/j.jde.2019.05.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the behavior of solutions of the Fisher-KPP equation when initial data decay slowly in space. First, we show by a comparison technique that the motion of an interface (or a thin transition layer) can be approximated as a level set of a first-order PDE of Hamilton-Jacobi type. Then by the method of characteristics, it is shown that various (but not all) motion of interfaces can be observed by taking initial data appropriately. Finally, we study the large-time behavior of solutions, especially, the existence of similarly expanding interfaces. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：4922 / 4947

页数：26

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