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  • © 2004

Reconstruction of Small Inhomogeneities from Boundary Measurements

Authors:

  1. Habib Ammari
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  2. Hyeonbae Kang
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1846)

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Table of contents (19 chapters)

  1. Front Matter

    Pages N2-IX
    PDF

  2. 1. Introduction

    • Habib Ammari, Hyeonbae Kang
    Pages 1-4

  3. Part I: Detection of Small Conductivity Inclusions

    • Habib Ammari, Hyeonbae Kang
    Pages 6-9

  4. 2. Transmission Problem

    • Habib Ammari, Hyeonbae Kang
    Pages 11-39

  5. 3. Generalized Polarization Tensors

    • Habib Ammari, Hyeonbae Kang
    Pages 41-64

  6. 4. Derivation of the Full Asymptotic Formula

    • Habib Ammari, Hyeonbae Kang
    Pages 65-78

  7. 5. Detection of Inclusions

    • Habib Ammari, Hyeonbae Kang
    Pages 79-101

  8. Part II: Detection of Small Elastic Inclusions

    • Habib Ammari, Hyeonbae Kang
    Pages 104-107

  9. 6. Transmission Problem for Elastostatics

    • Habib Ammari, Hyeonbae Kang
    Pages 109-127

  10. 7. Elastic Moment Tensor

    • Habib Ammari, Hyeonbae Kang
    Pages 129-149

  11. 8. Derivation of Full Asymptotic Expansions

    • Habib Ammari, Hyeonbae Kang
    Pages 151-157

  12. 9. Detection of Inclusions

    • Habib Ammari, Hyeonbae Kang
    Pages 159-173

  13. Part III: Detection of Small Electromagnetic Inclusions

    • Habib Ammari, Hyeonbae Kang
    Pages 176-178

  14. 10. Well-Posedness

    • Habib Ammari, Hyeonbae Kang
    Pages 179-183

  15. 11. Representation of Solutions

    • Habib Ammari, Hyeonbae Kang
    Pages 185-195

  16. 12. Derivation of Asymptotic Formulae

    • Habib Ammari, Hyeonbae Kang
    Pages 197-205

  17. 13. Reconstruction Algorithms

    • Habib Ammari, Hyeonbae Kang
    Pages 207-214

  18. A. Appendices

    • Habib Ammari, Hyeonbae Kang
    Pages 215-221

  19. References

    • Habib Ammari, Hyeonbae Kang
    Pages 223-236

  20. Index

    • Habib Ammari, Hyeonbae Kang
    Pages 237-238
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About this book

This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
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Keywords

  • Helmholtz equation
  • inverse boundary value problems
  • layer potential techniques
  • partial differential equation
  • reconstruction
  • small inhomogeneities
  • partial differential equations
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Reviews

From the reviews:

"The book … describes a ‘fresh and promising techniques for the reconstruction of small inclusions from boundary measurements’ and the presentation is ‘intended to be self-contained’. … The problems discussed in the book are of interest both theoretically and practically. This book hopefully will stimulate the research in the area of finding small inhomogeneities from experimental data." (Alexander G. Ramm, Zentralblatt MATH, Vol. 1113 (15), 2007)

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Bibliographic Information

  • Book Title: Reconstruction of Small Inhomogeneities from Boundary Measurements

  • Authors: Habib Ammari, Hyeonbae Kang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b98245

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2004

  • Softcover ISBN: 978-3-540-22483-9Published: 03 August 2004

  • eBook ISBN: 978-3-540-44501-2Published: 30 August 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 242

  • Topics: Differential Equations

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Access via your institution
eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-44501-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.95
Price excludes VAT (USA)
Learn about institutional subscriptions