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
收藏
页码：229 / 250
页数：22
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