Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 2

Global dynamics of the Brusselator equations

Pages: 167 – 196

DOI: https://dx.doi.org/10.4310/DPDE.2007.v4.n2.a4

Author

Yuncheng You (Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, U.S.A.)

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.

Keywords

Brusselator, Gray-Scott equation, global dynamics, global attractor, absorbing set, asymptotic compactness

2010 Mathematics Subject Classification

35B40, 35B41, 35K55, 35K57, 35Qxx, 37L30

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Published 1 January 2007