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Inverse Acoustic and Electromagnetic Scattering Theory

  • David Colton
  • Rainer Kress

Part of the Applied Mathematical Sciences book series (AMS, volume 93)

Table of contents

  1. Front Matter
    Pages I-X
  2. David Colton, Rainer Kress
    Pages 1-11
  3. David Colton, Rainer Kress
    Pages 12-36
  4. David Colton, Rainer Kress
    Pages 37-83
  5. David Colton, Rainer Kress
    Pages 84-103
  6. David Colton, Rainer Kress
    Pages 104-145
  7. David Colton, Rainer Kress
    Pages 146-187
  8. David Colton, Rainer Kress
    Pages 188-203
  9. David Colton, Rainer Kress
    Pages 204-237
  10. David Colton, Rainer Kress
    Pages 238-259
  11. David Colton, Rainer Kress
    Pages 260-292
  12. Back Matter
    Pages 293-307

About this book

Introduction

It has now been almost ten years since our first book on scattering theory ap­ peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti­ cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.

Keywords

Helmholtz equation acoustic waves electromagnetic electromagnetic wave electromagnetic waves inverse scattering scattering scattering theory

Authors and affiliations

  • David Colton
    • 1
  • Rainer Kress
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenFed. Rep. of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02835-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02837-7
  • Online ISBN 978-3-662-02835-3
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site