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Large-Time Behavior of Solutions of Linear Dispersive Equations

  • Book
  • © 1997

Overview

Authors:
  1. Daniel B. Dix
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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
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  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. Uniformly valid expansions as t→∞

    • Daniel B. Dix
    Pages 96-113

  5. Special results for special cases

    • Daniel B. Dix
    Pages 114-154

  6. Applications

    • Daniel B. Dix
    Pages 155-193

  7. Back Matter

    Pages 194-203
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Keywords

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.

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: Partial Differential Equations, Analysis, Fourier Analysis

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