Dynamics of Quasi-Stable Dissipative Systems

✍ Scribed by Igor Chueshov

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 405
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvii
Basic Concepts....Pages 1-45
General Facts on Dissipative Systems....Pages 47-90
Finite-Dimensional Behavior and Quasi-Stability....Pages 91-143
Abstract Parabolic Problems....Pages 145-218
Second Order Evolution Equations....Pages 219-283
Delay Equations in Infinite-Dimensional Spaces....Pages 285-348
Back Matter....Pages 349-390

✦ Subjects

Dynamical Systems and Ergodic Theory; Partial Differential Equations; Mathematical Methods in Physics