Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations by P. Constantin, C. Foias, B. Nicolaenko, R. Temam.

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer­ sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in...

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Bibliographic Details
Main Authors: Constantin, P. (Author), Foias, C. (Author), Nicolaenko, B. (Author), Temam, R. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1989.
Edition:1st ed. 1989.
Series:Applied Mathematical Sciences, 70
Springer eBook Collection.
Subjects:
Manifolds (Mathematics).
Complex manifolds.
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Preface
  • Acknowledgments
  • 1 Presentation of the Approach and of the Main Results
  • 2 The Transport of Finite-Dimensional Contact Elements
  • 3 Spectral Blocking Property
  • 4 Strong Squeezing Property
  • 5 Cone Invariance Properties
  • 6 Consequences Regarding the Global Attractor
  • 7 Local Exponential Decay Toward Blocked Integral Surfaces
  • 8 Exponential Decay of Volume Elements and the Dimension of the Global Attractor
  • 9 Choice of the Initial Manifold
  • 10 Construction of the Inertial Manifold
  • 11 Lower Bound for the Exponential Rate of Convergence to the Attractor
  • 12 Asymptotic Completeness: Preparation
  • 13 Asymptotic Completeness: Proof of Theorem 12.1
  • 14 Stability with Respect to Perturbations
  • 15 Application: The Kuramoto—Sivashinsky Equation
  • 16 Application: A Nonlocal Burgers Equation
  • 17 Application: The Cahn—Hilliard Equation
  • 18 Application: A Parabolic Equation in Two Space Variables
  • 19 Application: The Chaffee—Infante Reaction—Diffusion Equation
  • References.

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