Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

Sergey I. Kabanikhin; Abdigany D. Satybaev; Maxim A. Shishlenin

Sergey I. Kabanikhin, Abdigany D. Satybaev and Maxim A. Shishlenin

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

In: Inverse and Ill-Posed Problems Series, 48

De Gruyter | 2004

DOI: https://doi.org/10.1515/9783110960716

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About this book

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 methodand prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Frontmatter Free access PDF PDF	i
Preface Access restricted Content is available PDF PDF	v
Contents Free access PDF PDF	vii
Main definitions and notations Access restricted Content is available PDF PDF	1
Introduction Access restricted Content is available PDF PDF	3
Chapter 1. Finite-difference scheme inversion Access restricted Content is available PDF PDF	9
Chapter 2. Linearized multidimensional inverse problem for the wave equation Access restricted Content is available PDF PDF	37
Chapter 3. Methods of I. M. Gel’fand, Β. M. Levitan and M. G. Krein Access restricted Content is available PDF PDF	65
Chapter 4. Boundary control method Access restricted Content is available PDF PDF	119
Chapter 5. Projection method Access restricted Content is available PDF PDF	137
Appendix A Access restricted Content is available PDF PDF	163
Appendix Β Access restricted Content is available PDF PDF	167
Bibliography Access restricted Content is available PDF PDF	169

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

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