Inverse Problems for Kinetic and Other Evolution Equations

Yurii E. Anikonov, Sobolev Institute of Mathematics, Russian Academy of Sciences, Russia.

Introduction
Chapter 1. Formulas for solutions and coefficients of kinetic and other equations
Kinetic equations
Several formulas for solutions and coefficients of kinetic equations
Formulas in the inverse problems for kinetic equations with a potential
Formulas in tomography problems
Formulas of inverse problems for kinetic equation and integral geometry involving integration along geodesics
Differential and functional equations of inverse problems for nonlinear equations
Chapter 2. Theorems of uniqueness for inverse problems for kinetic equations
Inverse problem for a system of kinetic equations
Inverse problem for a system of quantum kinetic equations
On uniqueness of determination of a form by its integrals along geodesics
Dynamical model of the ethnic system. Formulas in direct and inverse problems
Chapter 3. Spherical harmonic method and inverse problem for kinetic equations
Spherical harmonic method
Steady-state transfer equation
Determining the dispersion index in the case of the P1-approximation
Definition of the dispersion index in the case of the P2-approximation
Reconstruction of the dispersion index and the source function
Chapter 4. Inverse problems for evolution equations of determining two coefficients
Nonlocal boundary-value problems for nonlinear equations and inverse problems of determining two coefficients
Recurrent formulas on derivatives of solutions
Integrodifferential equations in inverse problems of determining two coefficients for evolution equations
Inverse problem for a system of Maxwell equations
Determining two unknown coefficients of the parabolic-type equation
Inhomogeneous conditions of overdetermination
Representation of solutions and coefficients of partial differential equations of the second order
Chapter 5. Some results of multidimensional inverse problems theory
Formulas for coefficients in inverse problems for general evolutionary equations
Formulas in inverse problems for difference-differential equations
Inverse problems for evolutionary equations with degeneration and others
Group analysis and formulas in inverse problems of mathematical physics
Uniqueness of the solution of an integral equation of the first kind over real algebras with division of the finite dimension
Methods of geometry in the inverse seismic problem
Problems associated with projections of convex bodies onto planes
Bibliography