Dynamics of front solutions in a specific reaction-diffusion system in one dimension

被引：18

作者：

Ei, Shin-Ichiro ^{[1
]}

Ikeda, Hideo ^{[2
]}

Kawana, Takeyuki ^{[3
]}

机构：

[1] Kyushu Univ, Fac Math, Fukuoka 8108560, Japan

[2] Toyama Univ, Dept Math, Toyama 9308555, Japan

[3] Yokohama City Univ, Grad Sch Integrated Sci, Yokohama, Kanagawa 2360027, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2008年 / 25卷 / 01期

关键词：

reaction-diffusion systems; traveling fronts; pitch-fork bifurcation; heterogeneity;

D O I：

10.1007/BF03167516

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, two component reaction-diffusion systems with a specific bistable nonlinearity are concerned. The systems have the bifurcation structure of pitch-fork type of traveling front solutions with opposite velocities, which is rigorously proved and the ordinary differential equations describing the dynamics of such traveling front solutions are also derived explicitly. It enables us to know rigorously precise information on the dynamics of traveling front solutions. As an application of this result, the imperfection structure under small perturbations and the dynamics of traveling front solutions on heterogeneous media are discussed.

引用

页码：117 / 147

页数：31

共 18 条

[1] Pulse-pulse interaction in reaction-diffusion systems [J].