Standing Pulse Solutions in Reaction-Diffusion Systems with Skew-Gradient Structure

被引：28

作者：

Yanagida E. ^{[1
]}

机构：

[1] Mathematical Institute, Tohoku University

来源：

Journal of Dynamics and Differential Equations | 2002年 / 14卷 / 1期

基金：

日本学术振兴会;

关键词：

Evans function; Reaction-diffusion systems; Skew-gradient structure; Stability; Standing pulse solutions;

D O I：

10.1023/A:1012915411490

中图分类号：

学科分类号：

摘要：

The purpose of this paper is to introduce a reaction-diffusion system with "skew-gradient" structure and discuss the stability of standing pulse solutions. In short, the skew-gradient system is a reaction-diffusion system which resembles a gradient system but has nonlinearities with different sign. We assume the existence of a standing pulse solution and define its orientation in some geometrical manner. Then we show that the stationary solution becomes unstable if time constants satisfy some inequality. The Evans function plays a crucial role for the stability analysis. © 2002 Plenum Publishing Corporation.

引用

页码：189 / 205

页数：16

共 16 条

[11]

Maginu, K, Geometrical Condition for the Instability of Solitary Travelling Waves in Reaction-diffusion Systems

[12]

Ni W.-M., Takagi I., Point condensation generated by a reaction-diffusion system in axially symmetric domains, Japan J. Induslr. Appl. Math., 12, pp. 327-365, (1995)

[13]

Ni W.-M., Takagi I., Yanagida E., Stability Analysis of Point-condensation Solutions to A Reaction-diffusion System Proposed by Gierer and Meinhardt

[14]

Nishiura Y., Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit, Dynamics Reported, 3, pp. 25-103, (1994)

[15]

Takagi I., Point-condensation for a reaction-diffusion system, J. Differential Equations, 61, pp. 208-249, (1986)

[16]

Yanagida E., Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22, pp. 81-104, (1985)

← 1 2 →