Global dynamics of the Brusselator equations

Abstract

In this work the existence of a global attractor for the solution semiflow of the Brusselator equations is proved. A new decomposition method is introduced to overcome the difficulties in proving the asymptotical compactness of the coupled reaction-diffusion equations whose nonlinearity does not possess dissipative property. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. The existence of a global attractor with finite dimensionality is also shown by the same approach for the Gray-Scott equations, the Glycolysis equations, and the Schnackenberg equations.