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Finite- and infinite-dimensional attractors for porous media equations. (English) Zbl 1132.37027
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 $\epsilon$-entropy of infinite-dimensional attractors are also obtained.

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