# обратная задача

## Special Examples of Superstable Semigroups and Their Application in the Inverse Problems Theory

Special examples of superstable (quasinilpotent) semigroups and their application in the theory of linear inverse problems for evolutionary equations are studied. The term “semigroup” means here the semigroup of bounded linear operators of class C 0 . The standard research scheme is used. The linear inverse problem with the final overdetermination in a Banach space for the evolution equation is considered. A special assumption is introduced, related to the superstability of the main evolutionary semigroup.

## Recovering singular differential pencils with a turning point

Second-order pencils of differential equations on the half-line with turning points are considered. We establish properties of the spectrum and study the inverse spectral problem of recovering coefficients of the pencil from the spectral data.

## On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction for a Two-Part Layer

The coefficient inverse problem of thermal conductivity about the determination of the thermophysical characteristics of the functional-gradient part of a two-component layer is posed. The input information is the temperature measurement data on the top face of the layer. After the Laplace transform and dimensioning, the direct problem of heat conduction is solved on the basis of Galerkin projection method. Conversion of transformant on the basis of the theory of residues is carried out.