This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.

Vladimir G. Romanov, Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia.

One-dimensional inverse kinematics problem; inverse dynamical problem for a string; inverse problems for a layered medium; ray statements of inverse problems; posing of the inverse problems; asymptotic expansion; uniqueness theorems for the inverse problem; inverse problems related to a local heterogeneity; local solvability of some inverse problems; banach's spaces of analytic functions; determining coefficients of the lower terms; determining the speed of the sound; a regularization method for solving an inverse problem; inverse problems with single measurements; determining coefficient of the lowest term; determining coefficients under first derivatives; determining the speed of sound in the wave equation; case of a point source; stability estimates related to inverse problems for the transport equation; the problem of determining the relaxation and a density of inner sources; a stability estimate in the problem of determining the dispersion index and relaxation in 2D; the problem of determining the dispersion index and relaxation in 3D.