The ε-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors

Abstract

We prove an estimation of the Kolmogorov ε-entropy in H of the unitary ball in the space V, where H is a Hilbert space and V is a Sobolev-like subspace of H. Then, by means of Zelik’s result, an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.Junta de AndalucíaEuropean Commission, Excellent Science-European Research Counci