Inverse Problems of Mathematical Physics

Mikhail M. Lavrent'ev †; Alexander A. Avdeev, Institute of Computational Modeling, Russian Academy of Sciences, Krasnoyarsk, Russia;Mikhail M. Lavrent'ev (Jn.), Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia; Viatcheslav I. Priimenko,Universidade Estadual do Norte Fluminense Darcy Ribeiro, Campos dos Goytacazes, Brazil.

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 Lamé 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 Lamé 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