Dynamics of Partial Differential Equations
Volume 4 (2007)
Global dynamics of the Brusselator equations
Pages: 167 – 196
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.
Brusselator, Gray-Scott equation, global dynamics, global attractor, absorbing set, asymptotic compactness
2010 Mathematics Subject Classification
35B40, 35B41, 35K55, 35K57, 35Qxx, 37L30