Abstract
In this work the existence of a global attractor for the solution semio w of the Brusselator equations is proved. A new decomposition method is introduced to overcome the diculties in proving the asymptotical compact- ness of the coupled reaction-diusion equations whose nonlinearity does not possess dissipative property. It is proved that the Hausdor dimension and the fractal dimension of the global attractor are nite. The existence of a global attractor with nite dimensionality is also shown by the same approach for the Gray-Scott equations, the Glycolysis equations, and the Schnackenberg equations.
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