Existence and stability of multiple-spot solutions for the Gray-Scott model in R2

被引：53
作者：
Wei, JC
Winter, M
机构：
[1] Univ Stuttgart, Inst Math A, D-70569 Stuttgart, Germany
[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2003年 / 176卷 / 3-4期
关键词：
pattern formation; self-replication; spotty solutions; reaction-diffusion systems; REACTION-DIFFUSION SYSTEMS; GIERER-MEINHARDT SYSTEM; SELF-REPLICATING SPOTS; STIRRED TANK REACTOR; AUTOCATALYTIC REACTIONS; PATTERN-FORMATION; DYNAMICS;
D O I：
10.1016/S0167-2789(02)00743-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we rigorously prove the existence and stability of multiple-spot patterns for the Gray-Scott system in a two-dimensional domain which are far from spatial homogeneity. The Green's function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis. We establish a threshold behavior for stability: if a certain inequality for the parameters holds then we get stability, otherwise we get instability of multiple-spot solutions. The exact asymptotics of the critical thresholds are obtained. (C) 2002 Elsevier Science B.V All rights reserved.
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收藏
页码：147 / 180
页数：34
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