This monograph reports the advances that have
been made in the area by the author and many other mathematicians; it
is an important source of ideas for the researchers interested in the
subject.
—Zentralblatt MATH
Although advanced, this book is a very good
introduction to the subject, and the reading of the abstract part,
which is elegant, is pleasant. … this monograph will be of valuable
interest for those who aim to learn in the very rapidly growing
subject of infinite-dimensional dissipative dynamical
systems.
— Mathematical Reviews
This book is directed at researchers in nonlinear ordinary and partial
differential equations and at those who apply these topics to other fields
of science. About one third of the book focuses on the existence and
properties of the flow on the global attractor for a discrete or
continuous dynamical system. The author presents a detailed discussion of
abstract properties and examples of asymptotically smooth maps and
semigroups. He also covers some of the continuity properties of the global
attractor under perturbation, its capacity and Hausdorff dimension, and
the stability of the flow on the global attractor under perturbation. The
remainder of the book deals with particular equations occurring in
applications and especially emphasizes delay equations, reaction-diffusion
equations, and the damped wave equations. In each of the examples
presented, the author shows how to verify the existence of a global
attractor, and, for several examples, he discusses some properties of the
flow on the global attractor.