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Infinite dimensional attractors for porous medium equations in heterogeneous medium.
Math. Meth. Appl. Sci. 35, 1987-1996 (2012)
In this paper, we give a detailed study of the global attractors for porous medium equations in a heterogeneous medium. Not only the existence but also the infinite dimensionality of the global attractors is obtained by showing that their ϵ-Kolmogorov entropy behaves as a polynomial of the variable 1 ∕ ϵ as ϵ tends to zero, which is not observed for non-degenerate parabolic equations. The upper and lower bounds for the Kolmogorov ϵ-entropy of infinite-dimensional attractors are also obtained. We believe that the method developed in this paper has a general nature and can be applied to other classes of degenerate evolution equations.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
porous-medium equation; infinite dimensional global attractor; Kolmogorov ϵ-entropy
Language
english
Publication Year
2012
HGF-reported in Year
2012
ISSN (print) / ISBN
0170-4214
e-ISSN
1099-1476
Quellenangaben
Volume: 35,
Issue: 16,
Pages: 1987-1996
Publisher
Wiley
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)
PSP Element(s)
G-503800-002
DOI
10.1002/mma.2619
Scopus ID
84868206220
Erfassungsdatum
2012-09-26