Inverse Problems of Wave Processes
VSP International Science Publishers (Verlag)
978-90-6764-344-3 (ISBN)
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This monographcovers 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.
Aleksandr S. Blagoveshchenskii, Saint-Petersburg State University, Russia.
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
| Erscheint lt. Verlag | 26.3.2001 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series |
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 370 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 90-6764-344-0 / 9067643440 |
| ISBN-13 | 978-90-6764-344-3 / 9789067643443 |
| Zustand | Neuware |
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