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

共 50 条

[21] Diffusion-driven instability in reaction-diffusion systems
Wang, LC
Li, MY
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 254 (01) : 138 - 153
[22] Turing instability in reaction-diffusion systems with nonlinear diffusion
E. P. Zemskov
Journal of Experimental and Theoretical Physics, 2013, 117 : 764 - 769
[23] Breathing instability versus drift instability in a two-component reaction-diffusion system
Tarama, Mitsusuke
Ohta, Takao
Pismen, Len M.
PHYSICAL REVIEW E, 2011, 83 (01):
[24] REACTION-DIFFUSION WAVES IN THE VICINITY OF OBSTACLES - THE EIKONAL APPROACH
GIBBS, SP
GOMATAM, J
CHAOS SOLITONS & FRACTALS, 1995, 5 (3-4) : 543 - 553
[25] Disruption and recovery of reaction-diffusion wavefronts colliding with obstacles
Smith, Nathaniel J.
Glaser, Rebecca
Hui, Vincent W. H.
Lindner, John F.
Manz, Niklas
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2019, 517 : 307 - 320
[26] Wave instability and spatiotemporal chaos in reaction-diffusion system with oscillatory dynamics
Xie, FG
Yang, JZ
Li, HG
COMMUNICATIONS IN THEORETICAL PHYSICS, 2006, 45 (01) : 180 - 188
[27] Spatio-temporal patterns in a reaction-diffusion system with wave instability
Dolnik, M
Zhabotinsky, AM
Rovinsky, AB
Epstein, IR
CHEMICAL ENGINEERING SCIENCE, 2000, 55 (02) : 223 - 231
[28] Wave Instability and Spatiotemporal Chaos in Reaction-Diffusion System with Oscillatory Dynamics
XIE Fa-Gen~1 YANG Jun-Zhong~2 LI Hong-Gang~31 Research Department
Communications in Theoretical Physics, 2006, 45 (01) : 180 - 188
[29] Mobility-induced instability and pattern formation in a reaction-diffusion system
Riaz, SS
Kar, S
Ray, DS
JOURNAL OF CHEMICAL PHYSICS, 2004, 121 (11): : 5395 - 5399
[30] Turing instability and traveling fronts for a nonlinear reaction-diffusion system with cross-diffusion
Gambino, G.
Lombardo, M. C.
Sammartino, M.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2012, 82 (06) : 1112 - 1132

← 1 2 3 4 5 →