Inverse Problems of Kinetic and Other Evolution Equations

by Anikonov, Iu. E.; Anikonov, E.

• ISBN13: 9789067643450
• ISBN10: 9067643459
• Format: Hardcover
• Copyright: 2001-04-01
• Publisher: De Gruyter

Summary

This monographdeals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements. A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.

Table of Contents

Formulas for solutions and coefficients of kinetic and other equations	p. 1
Kinetic equations	p. 1
Several formulas for solutions and coefficients of kinetic equations	p. 5
Formulas in the inverse problems for kinetic equations with a potential	p. 9
Formulas in tomography problems	p. 11
Formulas of inverse problems for kinetic equation and integral geometry involving integration along geodesics	p. 15
Differential and functional equations of inverse problems for nonlinear equations	p. 21
Theorems of uniqueness for inverse problems for kinetic equations	p. 35
Inverse problem for a system of kinetic equations	p. 35
Inverse problems for a system of quantum kinetic equations	p. 40
On uniqueness of determination of a form by its integrals along geodesics	p. 55
Dynamical model of the ethnic system. Formulas in direct and inverse problems	p. 59
Spherical harmonic method and inverse problem for kinetic equations	p. 73
Spherical harmonics method	p. 73
Steady-state transfer equation	p. 79
Determining the dispersion index in the case of the P[subscript 1]-approximation	p. 93
Definition of the dispersion index in the case of the P[subscript 2]-approximation	p. 101
Reconstruction of the dispersion index and the source function	p. 121
Inverse problems for evolution equations of determining two coefficients	p. 127
Nonlocal boundary-value problems for nonlinear equations and inverse problems of determining two coefficients	p. 127
Recurrent formulas on derivatives of solutions	p. 139
Integrodifferential equations in inverse problems of determining two coefficients for evolution equations	p. 144
Inverse problem for a system of Maxwell equations	p. 152
Determining two unknown coefficients of the parabolic-type equation	p. 160
Inhomogeneous conditions of overdetermination	p. 172
Representation of solutions and coefficients of partial differential equations of the second order	p. 184
Some results of multidimensional inverse problems theory	p. 199
Formulas for coefficients in inverse problems for general evolutionary equations	p. 199
Formulas in inverse problems for difference-differential equations	p. 208
Inverse problem for evolutionary equations with degeneration and others	p. 212
Group analysis and formulas in inverse problems of mathematical physics	p. 216
Uniqueness of the solution of an integral equation of the first kind over real algebras with division of the finite dimension	p. 237
Methods of geometry in the inverse seismic problem	p. 244
Problems associated with projections of convex bodies onto planes	p. 252
Bibliography	p. 267
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