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Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

  • Michael Beals

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Michael Beals
    Pages 1-3
  3. Michael Beals
    Pages 4-29
  4. Michael Beals
    Pages 30-51
  5. Michael Beals
    Pages 52-73
  6. Michael Beals
    Pages 117-135
  7. Back Matter
    Pages 136-145

About this book

Introduction

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.

Keywords

DEX Microlocal analysis character equation interaction online operator proof university wave wave equation

Authors and affiliations

  • Michael Beals
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4554-4
  • Copyright Information Birkhäuser Boston 1989
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-3449-0
  • Online ISBN 978-1-4612-4554-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site