Pattern formation of a coupled two-cell Brusselator model
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 \(b\).
scientific article; zbMATH DE number 5687670
scientific article