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Dynamics of Evolutionary Equations

  • George R. Sell
  • Yuncheng You

Part of the Applied Mathematical Sciences book series (AMS, volume 143)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. George R. Sell, Yuncheng You
    Pages 1-9
  3. George R. Sell, Yuncheng You
    Pages 11-59
  4. George R. Sell, Yuncheng You
    Pages 61-140
  5. George R. Sell, Yuncheng You
    Pages 141-266
  6. George R. Sell, Yuncheng You
    Pages 267-358
  7. George R. Sell, Yuncheng You
    Pages 359-455
  8. George R. Sell, Yuncheng You
    Pages 457-568
  9. George R. Sell, Yuncheng You
    Pages 569-592
  10. Back Matter
    Pages 593-672

About this book

Introduction

The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi­ nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen­ dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.

Keywords

Dynamical Systems Dynamics of Nonlinear PDE's Evolutionary Equations Infinite Dynamical Systems Navier Stokes Dynamics calculus partial differential equation

Authors and affiliations

  • George R. Sell
    • 1
  • Yuncheng You
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5037-9
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3118-4
  • Online ISBN 978-1-4757-5037-9
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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