The Krasnosel'skij-Quittner Formula and Instability of a Reaction-Diffusion System with Unilateral Obstacles

被引：4

作者：

Kim, In-Sook ^{[1
]}

Vaeth, Martin ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[2] Free Univ Berlin, Math Inst, D-14195 Berlin, Germany

来源：

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 11卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

reaction-diffusion system; Signorini condition; unilateral obstacle; instability; asymptotic stability; Krasnoselskij formula; parabolic obstacle equation; BIFURCATION POINTS;

D O I：

10.4310/DPDE.2014.v11.n3.a2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a formula which relates the fixed point index of a parabolic obstacle equation to a fixed point index related to the right-hand side of the equation. The result is applied to a reaction-diffusion system at a constant equilibrium which is subject to Turing's diffusion-driven instability. It is shown that if a unilateral obstacle is added, the system becomes unstable in a parameter domain where the system without obstacle is stable.

引用

页码：229 / 250

页数：22

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