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Finite‐ and infinite‐dimensional attractors for porous media equations
Author(s) -
Efendiev M.,
Zelik S.
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm026
Subject(s) - attractor , mathematics , bounded function , fractal dimension , porous medium , entropy (arrow of time) , dimension (graph theory) , fractal , mathematical analysis , upper and lower bounds , pure mathematics , porosity , physics , thermodynamics , geotechnical engineering , engineering
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 ε‐entropy of infinite‐dimensional attractors are also obtained.