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Large-time Behavior of Solutions of Linear Dispersive Equations

  • Authors
  • Daniel B. Dix

Part of the Lecture Notes in Mathematics book series (LNM, volume 1668)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Daniel B. Dix
    Pages 1-74
  3. Daniel B. Dix
    Pages 75-95
  4. Daniel B. Dix
    Pages 96-113
  5. Daniel B. Dix
    Pages 114-154
  6. Daniel B. Dix
    Pages 155-193
  7. Back Matter
    Pages 194-203

About this book

Introduction

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.

Keywords

asymptotic expansions differential equation linear dispersive equations nonlinear wave equations oscillatory integrals partial differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093368
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63434-8
  • Online ISBN 978-3-540-69545-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site