Pattern formation of a coupled two-cell Brusselator model
type: Item
instance of: scholarly article
title: Pattern formation of a coupled two-cell Brusselator model
zbMATH Open document ID: 1195.35292
author: Jun Zhou
author: Chunlai Mu
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-03-29T00:00:00Z
review text: The authors study the asymptotic behavior (stability) and corresponding dynamics of the unique positive constant solution \((u,v,w,z)=(1,1,1,1)\) and give a priori positive upper and lower bounds to the positive solution for the system of nonlinear PDEs arising in the coupled two-cell model of a reaction-diffusion system with Brüsselator kinetics \[ \begin{cases} -d_1\Delta u=1-(b+1)u+bu^2v+c(w-u)& \text{in }\Omega,\\ -d_2\Delta v=u-u^2v & \text{in }\Omega\\ -d_1\Delta w=1+(b+1)w+bw^2z+c(u-w) & \text{in }\Omega,\\ -d_2\Delta z=w-w^2z & \text{in }\Omega,\\ \partial_n u=\partial_n v=\partial_n w=\partial_n z=0 & \text{on }\Omega. \end{cases} \] Also criteria of the existence and non-existences of positive non-constant solutions are given for varying values of the parameters \(d_1,d_2\) and \(b\).
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 92C15
zbMATH DE Number: 5687670
zbMATH Keywords: Brüsselator
zbMATH Keywords: two-cell model
zbMATH Keywords: pattern formation
zbMATH Keywords: a priori estimates
zbMATH Keywords: index
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: bifurcation
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.12.021
OpenAlex ID: W2021876284
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DOI: 10.1016/J.JMAA.2009.12.021
description: scientific article; zbMATH DE number 5687670