Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
1st Edition
Published on 9. April 2013
179 pages
978-3-11-096071-6 (ISBN)
Description
The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.
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Sergey I. Kabanikhin | Satybaev | Shishlenin
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
Book
12/2004
1st Edition
VSP International Science Publishers
€199.95
Article exhausted; check different version
Sergey I. Kabanikhin | Abdigany D. Satybaev | Maxim A. Shishlenin
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
Book
01/2004
1st Edition
De Gruyter
€299.00
Article exhausted; check different version
Sergey I. Kabanikhin | Abdigany D. Satybaev | Maxim A. Shishlenin
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
Book
De Gruyter
€109.95
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Content
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
