Inverse problems of mathematical physics
著者
書誌事項
Inverse problems of mathematical physics
（Inverse and ill-posed problems series）
VSP, 2003
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注記
Includes bibliographical references (p. [259]-275)
内容説明・目次
内容説明
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.
目次
Introduction
The concept of mathematical simulation
Direct and inverse problems
On correctness of direct and inverse problems of mathematical physics
Chapter 1. Some physical motivations of inverse problems
Inverse problems of geophysics
Inverse tomography problems
Chapter 2. Approximate methods of solution of ill-posed problems
On some aspects of statement and solution of ill-posed problems
Solutions on compact sets. The concept of a quasi-solution
The method of quasi-inversion
Regularization methods
Chapter 3. Integral geometry problems
Statement of integral geometry problems
The Radon problem
The problem of general form on the plane
Problems of general form in the space
Problems of Volterra type with manifolds invariant under the motion group
Integral geometry problems with perturbation on the plane
Mathematical problems of tomography and hyperbolic mappings
Chapter 4. One dimensional inverse problems
Some inverse problems for Lame system
Inverse problems for quasi-stationary Maxwell's equations
Connections among inverse problems of hyperbolic, elliptic and parabolic type
Problems with a focused source of disturbances
Reducing the problem with a focused source of disturbances to a linear integral equation: necessary and sufficient conditions for solvability of the inverse problems
Determination of the piece-wise constant coefficient for wave equation
Chapter 5. Inverse problems for the coupled Maxwell and Lame systems
One-dimensional inverse problem of electromagnetoelasticity in the case of the seismomagnetic effect
Inverse problems of electromagnetoelasticity in the case of piezoelectric interaction
Inverse problems of electromagnetoelasticity for weakly conducting media
An inverse problem of electromagnetoelasticity in the case of nonlinear interaction
Chapter 6. Numerical solution of inverse problems: some examples
Short review of numerical approaches to solving inverse problems
Numerical solution of a 3D inverse kinematic problem of seismics
Determination of the structure of the Earth's upper mantle
Numerical solution of inverse problems of electromagnetoelasticity
Simulation of the long-term coastal profile evolution
Bibliography
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