обратная задача

Recovering singular differential pencils with a turning point

Authors: Yurko V. A.

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

Authors: Vatulyan A. O., Nesterov S. A.

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.

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

Authors: Vu Nguyen Son Tung ..

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.

An Inverse Problem for Quasilinear Elliptic Equations

Authors: Aliev R. A.

The article examines incorrect return problems in the defining unknown factors in the quasilinear elliptic equation. Theorems of existence, uniqueness and stability have been proved. The consecutive approach method is used for the construction of the regulating algorithm for defining several factors.

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

Authors: Salimov R. B., Shabalin P. L.

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.

On Inverse Problem for Sturm – Liouville Operator with Discontinuous Coefficients

Authors: Akhmedova E. N., Guseinov I. M.

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.

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

Authors: Nabiev I.

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

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

Authors: Khromov A. A., Khromova G. V.

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.

Inverse Spectral Problem for Discrete Operators in Topological Spaces

Authors: Yurko V. A.

An inverse spectral problem for discrete operators of a triangular structure in topological spaces is studied. A constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for its solvability are obtained.

Numerical Solution of Inverse Spectral Problems for Sturm–Liouville Operators with Discontinuous Potentials

Authors: Efremova L. S.

We consider Sturm–Liouville differential operator with potential having a finite number of simple discontinuities. This paper is devoted to the numerical solution of such inverse spectral problems. The main result of this work is a procedure that is able to recover both the points of discontinuities as well as the heights of the jumps. Following, using these results, we may apply a suitable numerical method (for example, the generalized Rundell–Sacks algorithm with a special form of the reference potential) to reconstruct the potential more precisely.

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