Attractors of partial differential evolution equations and estimates of their dimension

Abstract

CONTENTS Introduction § 1. Maximal attractors of semigroups generated by evolution equations § 2. Examples of parabolic equations and systems having a maximal attractor § 3. The Hausdorff dimension of invariant sets § 4. Estimate of the change in volume under the action of shift operators generated by linear evolution equations § 5. An upper bound for the Hausdorff dimension of attractors of semigroups corresponding to evolution equations § 6. A lower bound for the dimension of an attractor § 7. Differentiability of shift operators § 8. Estimates of the Hausdorff dimension of an attractor of a two-dimensional Navier-Stokes system § 9. Upper and lower bounds for the Hausdorff dimension of attractors of parabolic equations and parabolic systems § 10. Attractors of semigroups having a global Lyapunov function § 11. Regular attractors of semigroups having a Lyapunov function References