Inverse Problems of Mathematical Physics

, by Lavrentev, M. M.; Avdeev, A. V.; Priimenko, V. I.

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ISBN: 9789067643962 | 9067643963
Cover: Hardcover
Copyright: 10/1/2003

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Thismonograph deals with the theory of inverse problems of mathematical physics andapplications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Introduction

(1)

The concept of mathematical simulation

(2)

Direct and inverse problems

(2)

On correctness of direct and inverse problems of mathematical physics

(8)

Some physical motivations of inverse problems

(16)

Inverse problems of geophysics

(9)

Inverse tomography problems

(7)

Approximate methods of solution of ill-posed problems

(24)

On some aspects of statement and solution of ill-posed problems

(1)

Solutions on compact sets. The concept of a quasi-solution

(11)

The method of quasi-inversion

(6)

Regularization methods

(6)

Integral geometry problems

(50)

Statement of integral geometry problems

(1)

The Radon problem

(4)

The problem of general form on the plane

(8)

Problems of general form in the space

(12)

Problems of Volterra type with manifolds invariant under the motion group

(4)

Integral geometry problems with perturbation on the plane

(7)

Mathematical problems of tomography and hyperbolic mappings

(15)

One dimensional inverse problems

103

(44)

Some inverse problems for Lame system

106

(6)

Inverse problems for quasi-stationary Maxwell's equations

112

(6)

Connections among inverse problems of hyperbolic, elliptic, and parabolic type

118

(7)

Problems with a focused source of disturbances

125

(10)

Reducing the problem with a focused source of disturbances to a linear integral equation: necessary and sufficient conditions for solvability of the inverse problems

135

(5)

Determination of the piece-wise constant coefficient for wave equation

140

(7)

Inverse problems for the coupled Maxwell and Lame systems

147

(44)

One-dimensional inverse problem of electromagnetoelasticity in the case of the seismomagnetic effect

148

(8)

Inverse problems of electromagnetoelasticity in the case of piezoelectric interaction

156

(9)

Inverse problems of electromagnetoelasticity for weakly conducting media

165

(14)

An inverse problem of electromagnetoelasticity in the case of nonlinear interaction

179

(12)

Numerical solution of inverse problems: some examples

191

(68)

Short review of numerical approaches to solving inverse problems

191

(5)

Numerical solution of a 3D inverse kinematic problem of seismics

196

(13)

Determination of the structure of the Earth's upper mantle

209

(20)

Numerical solution of inverse problems of electromagnet to elasticity

229

(16)

Simulation of the long-term coastal profile evolution

245

(14)

Bibliography

259

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Inverse Problems of Mathematical Physics

Summary

Table of Contents

Supplemental Materials