This book presents an expansion of the highly successful lectures given by Professor Ladyzhenskaya at the University of Rome, 'La Sapienza', under the auspices of the Accademia dei Lencei. The lectures were devoted to questions of the behaviour of trajectories for semi-groups of non-linear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many boundaries value problems for partial differential equations of a dissipative type. Professor Ladyzhenskaya was an internationally renowned mathematician and her lectures attracted large audiences. These notes reflect the high calibre of her lectures and should prove essential reading for anyone interested in partial differential equations and dynamical systems.
Preface; Part Inotions; 2. Semigroups of class K; 3. Semigroups of class AK; 4. On dimensions of compact invariant sets; Part II: Semigroups generated by evolution equations; 5. Introduction to Part II; 6. Estimates for the number of determining modes and the fractal dimension of bounded invariant sets for the Navier-Stokes equations; 7. Evolution equations of hyperbolic type; References; Index.