Infinite-dimensional attractors for evolution equations with $p$-Laplacian and their Kolmogorov entropy

Abstract

In this paper we give a detailed study on the attractors for the parabolic equations in bounded domains involving $p$-Laplacian as the principal term. Not only the existence of attractors but also their new properties are presented, which cannot be observed for the non-degenerate parabolic equations. In particular, we construct infinite-dimensional attractors whose $\varepsilon$-Kolmogorov entropy behave as the polynomial of $1/\varepsilon$ as $\varepsilon$ tends to zero.