# inverse problem

## Waves in a viscoelastic cylindrical waveguide with a defect

In this paper, we consider a direct problem on waves in a viscoelastic inhomogeneous cylindrical waveguide with annular delamination and investigate an inverse problem on the identification of the delamination parameters on the basis of the additional data on the displacement field at the outer boundary of the waveguide. In order to account rheological properties within the framework of the complex modules concept, we use a model of a standard viscoelastic body.

## The Solution of the Problem of Determining the Density of Heat Sources in a Rod

We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known.

## On Inverse Problem for Sturm – Liouville Operator with Discontinuous Coefﬁcients

In the paper uniqueness of reconstruction of the Sturm – Liouville operator with discontinuous coefﬁcients by spectral data is proved and algorithm of construction of the potential is provided.

## The M.A. Lavrentiev Inverse Problem on Mapping of Half-Plane Onto Polygon with Infinite Set of Vertices

The authors consider a generalization of the M.A.Lavrentiev inverse problem on a conformal mapping of half-plane onto interiority of a polygon for the case where the set of vertices of this polygon is infinite. We assume that the inner angles at unknown vertices and the image of the vertices under the conformal mapping on the real line are given. Under certain restrictions on values of the angles and on the sequence of points of the real line that are preimages of the vertices the formula for such a mapping is obtained.

## Solution of Inverse Problem for the Diffusion Operator in a Symmetric Case

In the paper uniqueness of reconstruction of the diffusion operator by aspectrum is proved and sufﬁcient solvability conditions are provided.

## 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.