This book is devoted to background material and recently developed
mathematical methods in the study of infinite-dimensional
dissipative systems. The theory of such systems is motivated by the
long-term goal to establish rigorous mathematical models for
turbulent and chaotic phenomena. The aim here is to offer general
methods and abstract results pertaining to fundamental dynamical
systems properties related to dissipative long-time behavior. The
book systematically presents, develops and uses the quasi-stability
method while substantially extending it by including for
consideration new classes of models and PDE systems arising in
Continuum Mechanics. The book can be used as a textbook in
dissipative dynamics at the graduate level. Igor Chueshov is a
Professor of Mathematics at Karazin Kharkov National University in
Kharkov, Ukraine.
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