Abildayeva, A. D. Kaparova, R. M. Assanova, A. T.
Published in
Lobachevskii Journal of Mathematics

AbstractProblem with integral condition for Fredholm integro-differential equation is considered. Conditions for a unique solvability of problem with integral condition for Fredholm integro-differential equation are established by method of introducing parameter. Results are illustrated to problem for Fredholm integro-differential equation with int...

Usmanov, K. I. Nazarova, K. Zh. Yerkisheva, Zh. S.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory transformation. The parameterization method is applied to the boundary value problem for a system with continuous kernel. By using the properties of involutory transformation, the problem is transformed to a boundar...

Yuldashev, T. K. Apakov, Yu. P. Zhuraev, A. Kh.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider the questions of the unique solvability of a boundary value problem for a third-order partial integro-differential equation with a degenerate kernel and multiple characteristics. An explicit solution of the boundary value problem is constructed. In this case, a combination of three methods was used: the method for...

Yuldashev, T. K.
Published in
Lobachevskii Journal of Mathematics

AbstractIn the three-dimensional domain a Boussinesq type nonlinear partial integro-differential equation of the fourth order with a degenerate kernel, integral form conditions, spectral parameters and reflecting argument is considered. The solution of this partial integro-differential equation is studied in the class of generality functions. The m...

Yuldashev, T. K.
Published in
Lobachevskii Journal of Mathematics

The problems of solvability and construction of solutions of a nonlocal boundary value problem for the second-order Fredholm integro-differential equation with degenerate kernel, integral conditions, spectral parameters and reflecting deviation are considered. Using the method of the degenerate kernel, the boundary value problem is integrated as an...

Yuldashev, T. K.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe problems of the existence and construction of solutions of a nonlocal boundary value problem for the homogeneous second-order Fredholm integrodifferential equation with a degenerate kernel and with two spectral parameters are considered. The singularities arising from the definition of arbitrary (unknown) constants are studied. The valu...

Yuldashev, T. K.
Published in
Lobachevskii Journal of Mathematics

In this paper are considered the questions of unique solvability and redefinitions of a nonlocal inverse problem for the Fredholm integro-differential equation of the second order with degenerate kernel, integral condition, and spectral parameter. Calculations of the value of the spectral parameter are reduced to the solve of trigonometric equation...

Yuldashev, T. K.
Published in
Lobachevskii Journal of Mathematics

This article examines questions of unique solvability for an inverse boundary value problem to recover the coefficient and boundary regime of a nonlinear integro-differential equation with degenerate kernel. We propose a novel method of degenerate kernel for the case of inverse boundary value problem for the considered ordinary integro-differential...

Chen, Jeng-Tzong Lee, Jia-Wei Tu, Ya-Ching
Published in
Earthquake Engineering and Engineering Vibration

In this study, the null-field boundary integral equation method (BIEM) and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degene...

Yuldashev, T. K.
Published in
Russian Mathematics

We consider the problem on the unique solvability of the inverse problem for a nonlinear partial Benney–Luke type integro-differential equation of the fourth order with a degenerate kernel. We modify the degenerate kernelmethod which has been designed for Fredholm integral equations of the second kind to apply to the case of the above-mentioned equ...