Investigation Methods for Inverse Problems

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.