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 ?‐Kolmogorov entropy behaves as a polynomial of the variable 1 ∕ ? as ? tends to zero, which is not observed for non‐degenerate parabolic equations. The upper and lower bounds for the Kolmogorov ?‐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.