Von Karman Evolution Equations

Well-posedness and Long Time Dynamics

  • Igor Chueshov
  • Irena Lasiecka

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Well-Posedness

    1. Front Matter
      Pages 11-11
    2. Igor Chueshov, Irena Lasiecka
      Pages 13-58
    3. Igor Chueshov, Irena Lasiecka
      Pages 59-128
    4. Igor Chueshov, Irena Lasiecka
      Pages 129-194
    5. Igor Chueshov, Irena Lasiecka
      Pages 195-242
    6. Igor Chueshov, Irena Lasiecka
      Pages 243-272
    7. Igor Chueshov, Irena Lasiecka
      Pages 273-334
  3. Long-Time Dynamics

    1. Front Matter
      Pages 335-335
    2. Igor Chueshov, Irena Lasiecka
      Pages 337-390
    3. Igor Chueshov, Irena Lasiecka
      Pages 391-446
    4. Igor Chueshov, Irena Lasiecka
      Pages 447-538
    5. Igor Chueshov, Irena Lasiecka
      Pages 539-624
    6. Igor Chueshov, Irena Lasiecka
      Pages 625-651
    7. Igor Chueshov, Irena Lasiecka
      Pages 653-694
    8. Igor Chueshov, Irena Lasiecka
      Pages 695-724
  4. Back Matter
    Pages 725-766

About this book

Introduction

The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presented here are the outgrowth of very recent studies by the authors, including a number of new original results here in print for the first time authors have provided a comprehensive and reasonably self-contained exposition of the general topic outlined above. This includes supplying all the functional analytic framework along with the function space theory as pertinent in the study of nonlinear plate models and more generally second order in time abstract evolution equations. While von Karman evolutions are the object under considerations, the methods developed transcendent this specific model and may be applied to many other equations, systems which exhibit similar hyperbolic or ultra-hyperbolic behavior (e.g. Berger's plate equations, Mindlin-Timoschenko systems, Kirchhoff-Boussinesq equations etc). In order to achieve a reasonable level of generality, the theoretical tools presented in the book are fairly abstract and tuned to general classes of second-order (in time) evolution equations, which are defined on abstract Banach spaces. The mathematical machinery needed to establish well-posedness of these dynamical systems, their regularity and long-time behavior is developed at the abstract level, where the needed hypotheses are axiomatized. This approach allows to look at von Karman evolutions as just one of the examples of a much broader class of evolutions. The generality of the approach and techniques developed are applicable (as shown in the book) to many other dynamics sharing certain rather general properties. Extensive background material provided in the monograph and self-contained presentation make this book suitable as a graduate textbook.

Keywords

Von Karman equations differential equation global attractors inertial manifolds long-time behavior rates of stabilization well-posedness

Authors and affiliations

  • Igor Chueshov
    • 1
  • Irena Lasiecka
    • 2
  1. 1.Dept. Mechanics & MathematicsKharkov National UniversityKharkovUkraine
  2. 2.Dept. MathematicsUniversity of VirginiaCharlottesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-87712-9
  • Copyright Information Springer Science+Business Media 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87711-2
  • Online ISBN 978-0-387-87712-9
  • Series Print ISSN 1439-7382
  • About this book