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Infinite-Dimensional Dynamical Systems in Mechanics and Physics

  • Textbook
  • © 1997

Overview

Authors:
  1. Roger Temam

    1. Laboratoire d’Analyse Numérique, Université Paris Sud, Orsay, France
      The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 68)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxi
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  2. General Introduction. The User’s Guide

    • Roger Temam
    Pages 1-14

  3. General Results and Concepts on Invariant Sets and Attractors

    • Roger Temam
    Pages 15-42

  4. Elements of Functional Analysis

    • Roger Temam
    Pages 43-81

  5. Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations

    • Roger Temam
    Pages 82-178

  6. Attractors of Dissipative Wave Equations

    • Roger Temam
    Pages 179-334

  7. Lyapunov Exponents and Dimension of Attractors

    • Roger Temam
    Pages 335-379

  8. Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems

    • Roger Temam
    Pages 380-464

  9. Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions

    • Roger Temam
    Pages 465-497

  10. The Cone and Squeezing Properties. Inertial Manifolds

    • Roger Temam
    Pages 498-535

  11. Inertial Manifolds and Slow Manifolds. The Non-self-adjoint Case

    • Roger Temam
    Pages 536-564

  12. Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds

    • Roger Temam
    Pages 565-584

  13. Back Matter

    Pages 585-650
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Keywords

About this book

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

Authors and Affiliations

  • Laboratoire d’Analyse Numérique, Université Paris Sud, Orsay, France

    Roger Temam

  • The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, USA

    Roger Temam

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