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Inverse Problems for Partial Differential Equations

  • Book
  • © 1998

Overview

Authors:
  1. Victor Isakov

    1. Department of Mathematics and Statistics, The Wichita State University, Wichita, USA

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  • This book is a comprehensive description of the current theoretical and numerical aspects of a particular type of partial differential equations.
  • Material is presented in a readable and informative manner.
  • Real-world applications are presented.
  • Level is accessible to both scientific and engineering researchers and graduate students.
  • Includes significant work done in this area in recent years.
  • Topics are related to broader themes in mathematical analysis.
  • Includes exercises and an extensive bibliography.

Part of the book series: Applied Mathematical Sciences (AMS, volume 127)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Inverse Problems

    • Victor Isakov
    Pages 1-19

  3. Ill-Posed Problems and Regularization

    • Victor Isakov
    Pages 20-38

  4. Uniqueness and Stability in the Cauchy Problem

    • Victor Isakov
    Pages 39-72

  5. Elliptic Equations. Single Boundary Measurements

    • Victor Isakov
    Pages 73-104

  6. Elliptic Equations: Many Boundary Measurements

    • Victor Isakov
    Pages 105-143

  7. Scattering problems

    • Victor Isakov
    Pages 144-162

  8. Integral Geometry and Tomography

    • Victor Isakov
    Pages 163-183

  9. Hyperbolic Problems

    • Victor Isakov
    Pages 184-217

  10. Inverse parabolic problems

    • Victor Isakov
    Pages 218-246

  11. Some Numerical Methods

    • Victor Isakov
    Pages 247-264

  12. Back Matter

    Pages 265-286
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Keywords

About this book

This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub­ stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica­ tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com­ plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.

Authors and Affiliations

  • Department of Mathematics and Statistics, The Wichita State University, Wichita, USA

    Victor Isakov

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