---

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.

---

Preface.- Introduction.- Basic Concepts.- General Facts on Dissipative Systems.- Finite-Dimensional Behavior and Quasi-Stability.- Abstract Parabolic Problems.- Second Order Evolution Equations.- Delay equations in infinite-dimensional spaces.- Auxiliary Facts.- References.- Index.

---

"This monograph brings together several important and interesting models of infinite dimensional dimensional evolutionary equations, studied from the long-term dynamics and stability point of view, from abstract parabolic problems, such as 2D hydrodynamical systems and Hopf´s models of turbulence, to second order evolution equations and delay equations. All the models are presented with clear and rigorous mathematical theory, which is beautifully developed along two chapters. ... This work is indeed a ´must have´ for mathematicians studying PDE models." (Matheus Cheque Bortolan, zbMATH 1362.37001, 2017)

"In this monograph, the author presents the general theory and applications of the dynamics of infinite-dimensional quasi-stable dissipative systems. ... The book is very well written, and the presentation is clear and rigorous. This monograph will be useful to researchers and graduate students interested in infinite-dimensional dissipative dynamical systems." (Rodica Luca, Mathematical Reviews, April, 2016)

---

Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.

---