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.