Formulas in Inverse and Ill-Posed Problems

Part 1 Equations and relations in inverse and ill-posed problems: general approach in a theory of multidimensional inverse problems; control and inverse problems; generating functions, evolution equation and inverse problems; algebraic question on the theory of multidimensional inverse problems for non-linear evolution equations; inverse problems for the Maxwell equation. Part 2 Formulas in inverse problems for evolution equations of the general type: inverse problem, formal results; sufficient conditions for correctness of the formulas (2.3), (2.4); the formulas for solution of the inverse problem in bounded domain; formulas in the inverse problem for a general evolution equation of the second order; reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces; reduction of more common inverse problems to initial-boundary value problems; formulas in problems of determination of sources. Part 4 Formulas in inverse problems for the kinematic problems in seismology: inverse kinematic problem - some relations; formulas for the ray and time; integro-differential relations and the first integrals; linear first integral quadratic first-integral generalization of the Herglotz formula; integro-differential identities in the plane; determination of the Riemann metric of a special form; the problem associated with an equation for geodesics of the Liouville metric; determination of a homogeneous functional. Part 3 Formulas in integral geometry and tomography. Part 4 The analytical representation of solutions of some inverse and ill-posed problems. Part 5 Mathematical models in the problems of ethnogeny and evolution of populations. (Part contents)