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.

Can be used as a textbook for courses in dissipative dynamics at the graduate level Contains a large number of exercises Presents, develops and uses the quasi-stability method Useful not only to mathematicians interested in the general theory of dynamical systems, but also to physicists and engineers interested in mathematical background and methods for the asymptotic analysis of infinite-dimensional dissipative systems that arise in Continuum Mechanics Includes supplementary material: sn.pub/extras

Autorentext

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

Inhalt
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.