Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

обратная задача

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.

Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for Sturm–Liouville Operators with a Nonintegrable Singularity Inside a Finite Interval

The inverse spectral problem of recovering Sturm–Liouville operators on a finite interval with a nonintegrable Bessel-type singularity in an interior point from the given spectral data is studied. A corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for the solvability of the inverse problem are obtained.

Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point

The inverse problem of recovering Sturm–Liouville operators on the half-line with a nonintegrable Bessel-type singularity in an interior point from the given Weyl function is studied. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions of the solvability of the inverse problem are obtained. 

Inverse Spectral Problem for Discrete Operators in Topological Spaces

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

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.

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.

An Inverse Problem for Quasilinear Elliptic Equations

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.

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