интегральное уравнение

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.

A Boundary-Value Problem with Shifted for a Mixed Type Equation with Fractional Derivative

Authors: Repin O. A., Sayganova S. A.

A non-local problem for a mixed type equation with partial fractional derivative of Riemann – Liouville is studied, boundary condition of which contains linear combination of generalized operators of fractional integro-differentiation. Unique solvability of the problem is then proved.

Approximating Properties of the Powers of the Differentiation Operator Resolvent

Authors: Khromov A. A.

The families of operators are constructed and their approximating properties are investigated in the problems of approximating the derivative of function sand the smooth solutions of integralequations.

Solution of Integral Equations via Resolvents of Simplest Differential Operators

Authors: Khromov A. A.

Families of operators for approximate solution of integral equations with unbounded inverse operators and right parts of equations specified by the root-mean-square approximations are constructed.