Infinite-dimensional attractors for parabolic equations with \(p\)-Laplacian in heterogeneous medium
The authors study the global attractors for a class of \(p\)-Laplacian parabolic equations in a heterogeneous medium. Not only the existence but also the infinite dimensionality of the global attractors is presented by showing that their \(\varepsilon \)-Kolmogorov entropy behaves as a polynomial of the variable \(1/\varepsilon \) as \(\varepsilon\) tends to zero, which is not observed for non-degenerate parabolic equations. The upper and lower bounds for the \(\varepsilon \)-Kolmogorov entropy of infinite-dimensional attractors are also obtained.
scientific article; zbMATH DE number 5956010