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Proceedings of the London Mathematical Society Advance Access originally published online on August 11, 2007
Proceedings of the London Mathematical Society 2008 96(1):51-77; doi:10.1112/plms/pdm026
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© 2007 London Mathematical Society

Finite- and infinite-dimensional attractors for porous media equations

M. Efendiev

GSF/Technical University Munich Center of Mathematical Sciences Boltzmann strasse 3 85747 Garching/Munich Germany efendiev{at}math.fu-berlin.de

S. Zelik

Department of Mathematics University of Surrey Guildford GU2 7XH United Kingdom

Received 8 March 2006. Revision received 16 February 2007.

The fractal dimension of the global attractors of porous media equations in bounded domains is studied. The conditions which guarantee this attractor to be finite dimensional are found and the examples of infinite-dimensional attractors that do not satisfy these conditions are constructed. The upper and lower bounds for the Kolmogorov {varepsilon}-entropy of infinite-dimensional attractors are also obtained.

This research is partially supported by the Alexander von Humboldt foundation.


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