Inverse Problems for Kinetic and Other Evolution Equations

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; grou p 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.