Mathematics – Analysis of PDEs
Scientific paper
2011-02-19
Mathematics
Analysis of PDEs
30 pages
Scientific paper
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling between two compartments. The method of grouping and re-scaling estimation is developed to deal with the challenge in proving the absorbing property and the asymptotic compactness of this typical multi-component reaction-diffusion systems. It is also proved that the global attractor is an $(H, E)$ global attractor with the $L^\infty$ regularity and that the Hausdorff dimension and the fractal dimension of the global attractor are finite. The results and methodology can find many applications and further extensions in complex biological and biochemical dynamical systems.
You Yuncheng
Zhou Shengfan
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