Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

  • P. Constantin
  • C. Foias
  • B. Nicolaenko
  • R. Teman

Part of the Applied Mathematical Sciences book series (AMS, volume 70)

Table of contents

  1. Front Matter
    Pages i-x
  2. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 1-3
  3. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 4-14
  4. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 15-20
  5. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 21-24
  6. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 25-28
  7. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 29-32
  8. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 33-35
  9. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 36-37
  10. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 38-41
  11. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 42-46
  12. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 47-51
  13. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 52-54
  14. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 55-60
  15. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 61-67
  16. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 68-71
  17. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 72-81
  18. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 82-90
  19. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 91-104
  20. P. Constantin, C. Foias, B. Nicolaenko, R. Teman
    Pages 105-110

About this book

Introduction

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 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani­ folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ­ ential equations.

Keywords

convergence differential equation integral manifold partial differential equation stability

Authors and affiliations

  • P. Constantin
    • 1
  • C. Foias
    • 2
  • B. Nicolaenko
    • 3
  • R. Teman
    • 4
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA
  3. 3.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  4. 4.Department de MathematiquesUniversité de Paris-SudOrsayFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3506-4
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8131-3
  • Online ISBN 978-1-4612-3506-4
  • Series Print ISSN 0066-5452
  • About this book
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