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Inverse Acoustic and Electromagnetic Scattering Theory

  • Book
  • © 1992

Overview

Authors:
  1. David Colton

    1. Department of Mathematical Sciences, University of Delaware, Newark, USA

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  2. Rainer Kress

    1. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, Fed. Rep. of Germany

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • David Colton, Rainer Kress
    Pages 1-11

  3. The Helmholtz Equation

    • David Colton, Rainer Kress
    Pages 12-36

  4. Direct Acoustic Obstacle Scattering

    • David Colton, Rainer Kress
    Pages 37-83

  5. Ill-Posed Problems

    • David Colton, Rainer Kress
    Pages 84-103

  6. Inverse Acoustic Obstacle Scattering

    • David Colton, Rainer Kress
    Pages 104-145

  7. The Maxwell Equations

    • David Colton, Rainer Kress
    Pages 146-187

  8. Inverse Electromagnetic Obstacle Scattering

    • David Colton, Rainer Kress
    Pages 188-203

  9. Acoustic Waves in an Inhomogeneous Medium

    • David Colton, Rainer Kress
    Pages 204-237

  10. Electromagnetic Waves in an Inhomogeneous Medium

    • David Colton, Rainer Kress
    Pages 238-259

  11. The Inverse Medium Problem

    • David Colton, Rainer Kress
    Pages 260-292

  12. Back Matter

    Pages 293-307
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematical Sciences, University of Delaware, Newark, USA

    David Colton

  • Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, Fed. Rep. of Germany

    Rainer Kress

Bibliographic Information

  • Book Title: Inverse Acoustic and Electromagnetic Scattering Theory

  • Authors: David Colton, Rainer Kress

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-02835-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • eBook ISBN: 978-3-662-02835-3Published: 17 April 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: X, 307

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Analysis, Numerical Analysis

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