Infinite dimensional attractors for porous medium equations in heterogeneous medium

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. Copyright © 2012 John Wiley & Sons, Ltd.