Applied Mathematical Sciences

Inverse Problems for Partial Differential Equations

Authors: Isakov, Victor

  • 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.

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eBook $69.99
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  • ISBN 978-1-4899-0030-2
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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.

Table of contents (10 chapters)

  • Inverse Problems

    Isakov, Victor

    Pages 1-19

  • Ill-Posed Problems and Regularization

    Isakov, Victor

    Pages 20-38

  • Uniqueness and Stability in the Cauchy Problem

    Isakov, Victor

    Pages 39-72

  • Elliptic Equations. Single Boundary Measurements

    Isakov, Victor

    Pages 73-104

  • Elliptic Equations: Many Boundary Measurements

    Isakov, Victor

    Pages 105-143

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4899-0030-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Inverse Problems for Partial Differential Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
127
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4899-0030-2
DOI
10.1007/978-1-4899-0030-2
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XI, 286
Number of Illustrations and Tables
1 b/w illustrations
Topics