Electron. J. Diff. Equ., Vol. 2011 (2011), No. 25, pp. 1-28.

Global dynamics of a reaction-diffusion system

Yuncheng You

In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.

Submitted July 28, 2010. Published February 10, 2011.
Math Subject Classifications: 37L30, 35B40, 35B41, 35K55, 35K57, 80A32, 92B05.
Key Words: Reaction-diffusion system; Brusselator; two-cell model; global attractor; absorbing set; asymptotic compactness; exponential attractor.

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Yuncheng You
Department of Mathematics and Statistics
University of South Florida
Tampa, FL 33620, USA
email: you@mail.usf.edu

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