Inverse Problems for Partial Differential Equations

  • Victor Isakov

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Victor Isakov
    Pages 1-19
  3. Victor Isakov
    Pages 20-38
  4. Victor Isakov
    Pages 144-162
  5. Victor Isakov
    Pages 163-183
  6. Victor Isakov
    Pages 184-217
  7. Victor Isakov
    Pages 218-246
  8. Victor Isakov
    Pages 247-264
  9. Back Matter
    Pages 265-286

About this book

Introduction

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.

Keywords

differential equation hyperbolic equation mathematical analysis numerical methods partial differential equation

Authors and affiliations

  • Victor Isakov
    • 1
  1. 1.Department of Mathematics and StatisticsThe Wichita State UniversityWichitaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-0030-2
  • Copyright Information Springer-Verlag New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-0032-6
  • Online ISBN 978-1-4899-0030-2
  • Series Print ISSN 0066-5452
  • About this book