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Infinite-dimensional attractors for evolution equations with \(p\)-Laplacian and their Kolmogorov entropy. (English) Zbl 1212.37081

Summary: 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.

MSC:

37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35K65 Degenerate parabolic equations
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