On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators

Anh Cung The and Toi Vu Manh

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-27

Abstract:

We study the long-time behavior of solutions to nonautonomous semilinear parabolic systems involving the Grushin operators in bounded domains. We prove the existence of a pullback -attractor in for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback -attractor is more regular and has a finite fractal dimension. The obtained results, in particular, extend and improve some existing ones for the reaction-diffusion equations and the Grushin equations.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:178057

DOI: 10.1155/2011/178057

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