Okboev, A. B.
Published in
Lobachevskii Journal of Mathematics

AbstractIn the work Tricomi problem was investigated for a parabolic-hyperbolic type equation in a mixed domain. If the parabolic degeneration line is a characteristic of a hyperbolic equation, then Tricomi problem for considered equation will not be uniquely solvable. Therefore, another formulation of Tricomi problem was proposed which the gluing ...

Urinov, A. K. Karimov, Sh. T.
Published in
Lobachevskii Journal of Mathematics

AbstractThe Cauchy problem for an iterated generalized two-axially symmetric equation of hyperbolic type is investigated. Unlike traditional methods, the generalized Erdélyi–Kober operator of fractional order is applied to solve the problem. The application of this operator allows us to reduce the equations with the lowest term and with the singula...

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...

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

AbstractWe consider a three-dimensional elliptic equation with two singular coefficients, for which a nonlocal problem is studied in a semi-infinite parallelepiped. The study of the problem is carried out using the method of separation of Fourier variables and spectral analysis. For the problem posed, using the Fourier method, two one-dimensional s...

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

AbstractThe questions of weakly generalized solvability of a nonlinear inverse problem in nonlinear optimal control of thermal processes for a parabolic differential equation are studied. The parabolic equation is considered under initial and boundary conditions. To determine the recovery function, a nonlocal integral condition is specified. Moreov...

Karakeev, T. T. Imanaliev, T. M.
Published in
Lobachevskii Journal of Mathematics

AbstractWe study a regularization of linear Volterra integral equation of the first kind with differentiable kernel degenerated at the initial point or at the end point of the interval on the diagonal. Accordingly, in the first case, the kernel on the diagonal is a non-decreasing function, in the second case, a non-increasing function. Regularizing...

Omuraliev, A. S. Abylaeva, E. Esengul kyzy, P.
Published in
Lobachevskii Journal of Mathematics

AbstractThe work is devoted to the construction of the asymptotics of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains, along with parabolic boundary layer functio...

Kozhobekov, K. G. Erkebaev, U. Z. Tursunov, D. A.
Published in
Lobachevskii Journal of Mathematics

AbstractThe article studies the asymptotic behavior of the solutions of a singularly perturbed three boundary value problems on an interval. The object of the study is a linear inhomogeneous ordinary differential equation of the second order with a small parameter with the highest derivative of the unknown function. The singularities of the problem...

Yuldasheva, A. V.
Published in
Lobachevskii Journal of Mathematics

AbstractThe peridinamics theory, proposed by Silling in 2000, is a nonlocal theory of continuum mechanics based on an integro-differential equation without spatial derivatives and may cope with discontinuous displacement fields commonly occurring in fracture mechanics. Instead of spatial differential operators, integration over differences of the d...

Islomov, B. I. Usmonov, B. Z.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this research work, for a third-order elliptic-hyperbolic type equation, a method for studying a nonlocal boundary-value problem by solving the inverse problem for a second-order mixed elliptic-hyperbolic type equation with an unknown right-hand side was proposed. A new extremume principle for a third-order equation was developed, and wi...