Direct methods of solving multidimensional inverse hyperbolic problems
著者
書誌事項
Direct methods of solving multidimensional inverse hyperbolic problems
（Inverse and ill-posed problems series）
VSP, c2005
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注記
Includes bibliographical references (p. [169]-179)
内容説明・目次
内容説明
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
The problems of determining coefficients of hyperbolic equations and systems from additional information on their solutions are of great practical significance. As a rule, the desired coefficients are important characteristics of the media under consideration. In this monograph, dynamic type of inverse problems in which the additional information is given by the trace of the direct problem solution on a (usually time-like) surface of the domain is considered.
In this book theoretical and numerical background of the direct methods are discussed. Theorems of convergence, conditional stability and other properties of the mentioned above methods are formulated and proven.
目次
Main definitions and notations
Introduction
Chapter 1. Finite-difference scheme inversion (FDSI)
1.1. Introduction
1.2. Volterra operator equations
1.3. Definitions and examples
1.4. Convergence of FDSI
1.5. Numerical examples
Chapter 2. Linearized multidimensional inverse problem
for the wave equation
2.1. Introduction
2.2. Problem formulation
2.3. Linearization
2.4. Analyzing the structure of the solution to one-dimensional direct
problem
2.5. Existence theorem for the direct problem
2.6. Uniqueness of solutions to the inverse problem and regularization
2.7. Numerical examples
vi Direct Methods of Solving Multidimensional Inverse Problems
Chapter 3. Methods of I.M. Gel'fand, B.M. Levitan
and M. G. Krein
3.1. Introduction
3.2. Gel'fand-Levitan-Krein (GLK) equation for one-dimensional
inverse problem
3.3. Multidimensional analog of GLK-equations
3.4. Gel'fand-Levitan method for wave equation
3.5. Discrete analog of the Gel'fand-Levitan equation
3.6. Multidimensional discrete analog
3.7. Numerical examples
Chapter 4. Boundary control method (BC method)
4.1. Introduction. Statement of the problem
4.2. BC method in one-dimensional case
4.3. BC method for 2D acoustic inverse problem
4.4. Numerical examples
Chapter 5. Projection method
5.1. Introduction
5.2. Projection method for solving inverse problem
for the wave equation
5.3. Projection method for solving inverse acoustic problem
5.4. Numerical examples
Appendix A
Appendix B
Bibliography
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