Inverse Problems for Kinetic and Other Evolution Equations

Inverse Problems for Kinetic and Other Evolution Equations

Pub. Date:
De Gruyter, Walter, Inc.


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Inverse Problems for Kinetic and Other Evolution Equations

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.

Product Details

ISBN-13: 9789067643450
Publisher: De Gruyter, Walter, Inc.
Publication date: 03/28/2001
Series: Inverse and III-Posed Problems Series , #24
Pages: 270
Product dimensions: 6.30(w) x 9.45(h) x (d)
Age Range: 18 Years

About the Author

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

Table of Contents

Chapter 1.Formulas for solutions and coefficients of kinetic and other equations1
1.1.Kinetic equations1
1.2.Several formulas for solutions and coefficients of kinetic equations5
1.3.Formulas in the inverse problems for kinetic equations with a potential9
1.4.Formulas in tomography problems11
1.5.Formulas of inverse problems for kinetic equation and integral geometry involving integration along geodesics15
1.6.Differential and functional equations of inverse problems for nonlinear equations21
Chapter 2.Theorems of uniqueness for inverse problems for kinetic equations35
2.1.Inverse problem for a system of kinetic equations35
2.2.Inverse problems for a system of quantum kinetic equations40
2.3.On uniqueness of determination of a form by its integrals along geodesics55
2.4.Dynamical model of the ethnic system. Formulas in direct and inverse problems59
Chapter 3.Spherical harmonic method and inverse problem for kinetic equations73
3.1.Spherical harmonics method73
3.2.Steady-state transfer equation79
3.3.Determining the dispersion index in the case of the P[subscript 1]-approximation93
3.4.Definition of the dispersion index in the case of the P[subscript 2]-approximation101
3.5.Reconstruction of the dispersion index and the source function121
Chapter 4.Inverse problems for evolution equations of determining two coefficients127
4.1.Nonlocal boundary-value problems for nonlinear equations and inverse problems of determining two coefficients127
4.2.Recurrent formulas on derivatives of solutions139
4.3.Integrodifferential equations in inverse problems of determining two coefficients for evolution equations144
4.4.Inverse problem for a system of Maxwell equations152
4.5.Determining two unknown coefficients of the parabolic-type equation160
4.6.Inhomogeneous conditions of overdetermination172
4.7.Representation of solutions and coefficients of partial differential equations of the second order184
Chapter 5.Some results of multidimensional inverse problems theory199
5.1.Formulas for coefficients in inverse problems for general evolutionary equations199
5.2.Formulas in inverse problems for difference-differential equations208
5.3.Inverse problem for evolutionary equations with degeneration and others212
5.4.Group analysis and formulas in inverse problems of mathematical physics216
5.5.Uniqueness of the solution of an integral equation of the first kind over real algebras with division of the finite dimension237
5.6.Methods of geometry in the inverse seismic problem244
5.7.Problems associated with projections of convex bodies onto planes252

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