Inverse Problems of Wave Processes
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Book 1
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Inverse Problems of Wave Processes: (23 Inverse and Ill-Posed Problems Series)

Inverse Problems of Wave Processes: (23 Inverse and Ill-Posed Problems Series)


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About the Book

This volume studies dynamical inverse problems, that is problems whose data are the values of wave fields. It deals with the problem of determination of one or more coefficients of a hyperbolic equation or a system of hyperbolic equations. The desired coefficients are functions of point. Most attention is given to the case where the required functions depend only on one coordinate. The first chapter of the book deals mainly with methods of solution of one-dimensional inverse problems. The second chapter focuses on scalar inverse problems of wave propagation in a layered medium. In the final chapter inverse problems for elasticity equations in stratified media and acoustic equations for moving media are given. This monograph should be of value and interest to researchers in the fields of mathematical physics, geophysics, acoustics, elasticity theory, and electrodynamics.

Table of Contents:
Introduction Chapter 1. One-dimensional inverse problems Setting of a problem for string equation Peculiarities of solution. Formulation of the direct problem The first method of solution of inverse problem Method of linear integral equations The case of discontinuous σ(y) The Gel’fand-Levitan equation for second-order hyperbolic equations Some cases of explicit solution On connection of inverse problems with nonlinear ordinary differential equations The case of more general system of equations Chapter 2. Theory of inverse problems for wave processes in layered media Inverse problems of acoustics General second-order hyperbolic equations The scattering problem for the general hyperbolic equation Chapter 3. Inverse problems for vector wave processes Inverse problem for elasticity equation Inverse problem of sound propagation in a moving layered medium The case of one-dimensional sound propagation Inverse problems for hyperbolic systems Second order-hyperbolic system Bibliography

About the Author :
Aleksandr S. Blagoveshchenskii, Saint-Petersburg State University, Russia.


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Product Details
  • ISBN-13: 9789067643443
  • Publisher: Brill
  • Publisher Imprint: VSP International Science Publishers
  • Language: English
  • Series Title: 23 Inverse and Ill-Posed Problems Series
  • ISBN-10: 9067643440
  • Publisher Date: 26 Mar 2001
  • Binding: Hardback
  • No of Pages: 141
  • Weight: 370 gr


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Inverse Problems of Wave Processes: (23 Inverse and Ill-Posed Problems Series)
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