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Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

  • Book
  • © 1989

Overview

Authors:
  1. Michael Beals

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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Part of the book series: Progress in Mathematics (PM, volume 130)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Michael Beals
    Pages 1-3

  3. Nonlinear Microlocal Analysis

    • Michael Beals
    Pages 4-29

  4. Appearance of Nonlinear Singularities

    • Michael Beals
    Pages 30-51

  5. Conormal Singularities

    • Michael Beals
    Pages 52-73

  6. Conormal Regularity after Nonlinear Interaction

    • Michael Beals
    Pages 74-95

  7. Regularity and Singularities in Problems on Domains With Boundary

    • Michael Beals
    Pages 96-116

  8. Conormal Waves on Domains with Boundary

    • Michael Beals
    Pages 117-135

  9. Back Matter

    Pages 136-145
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Keywords

About this book

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen­ sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Authors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Michael Beals

Bibliographic Information

  • Book Title: Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

  • Authors: Michael Beals

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-4554-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1989

  • Softcover ISBN: 978-0-8176-3449-0Published: 01 November 1989

  • eBook ISBN: 978-1-4612-4554-4Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 145

  • Topics: Partial Differential Equations

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