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  • © 1997

Large-Time Behavior of Solutions of Linear Dispersive Equations

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XIV
  2. Laplace expansions, outer regions

    • Daniel B. Dix
    Pages 1-74
  3. Expansion in the inner region, matching

    • Daniel B. Dix
    Pages 75-95
  4. Special results for special cases

    • Daniel B. Dix
    Pages 114-154
  5. Applications

    • Daniel B. Dix
    Pages 155-193
  6. Back Matter

    Pages 194-203

About this book

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
  • partial differential equations

Bibliographic Information

  • Book Title: Large-Time Behavior of Solutions of Linear Dispersive Equations

  • Authors: Daniel B. Dix

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093368

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63434-8Published: 18 September 1997

  • eBook ISBN: 978-3-540-69545-5Published: 13 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 203

  • Topics: Differential Equations, Analysis, Fourier Analysis

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions