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Zbl 1132.37027
Efendiev, M.; Zelik, S.
Finite- and infinite-dimensional attractors for porous media equations. (English)
[J] Proc. Lond. Math. Soc. (3) 96, No. 1, 51-77 (2008). ISSN 0024-6115; ISSN 1460-244X/e

Summary: 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.

MSC 2000:: *37L30 Attractors and their dimensions
35K65 Parabolic equations of degenerate type
35K10 Second order parabolic equations, general

Keywords: fractal dimension; global attractors; Kolmogorov $\varepsilon$-entropy

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