Asan ÖMÜRALİEV | Ramiz RAFATOV

Article | 2011 | Automation and Remote Control72 ( 1 )

For the singularly perturbed parabolic problem, a regularized asymptotics of the solution of the problem of optimal control was constructed. The solution asymptotics involves parabolic boundary-layer functions obeying a special function called the “complementary probability integral.

Asan ÖMÜRALİEV

Article | 2006 | Журнал вычислительной математики и математической физики / Computational Mathematics and Mathematical Physics46 ( 8 )

Строится регуляризованная асимптотика решения сингулярно возмущенной двумерной параболической задачи в областях с угловыми точками границы. Асимптотика решения таких задач содержит как обыкновенные погранслойные функции, так и параболические погранслойные функции и их произведения, которые описывают угловой пограничный слой.

Asan ÖMÜRALİEV | Ella ABILAYEVA

Article | 2022 | Journal of Mathematical Sciences264 ( 4 )

In this paper we construct the asymptotics of the solution of the Cauchy problem for a singularly perturbed hyperbolic system by using the regularization method for singularly perturbed problems of S.A. Lomov. The regularization method for singularly perturbed problems of S.A. Lomov is used for the first time to construct the asymptotic solution of a hyperbolic system.

Asan ÖMÜRALİEV | Peyil Esengul Kızı

Article | 2021 | Lobachevskii Journal of Mathematics42 ( 15 )

The work is devoted to the construction of the asymptotic behavior 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 boundary layer functions.

Asan ÖMÜRALİEV

Article | 2019 | Дифференциальные уравнения55 ( 6 )

Изучается первая краевая задача для -мерной линейной системы дифференциальных уравнений параболического типа с малым параметром при пространственной производной. Построена полная регуляризованная асимптотика решения в случае, когда система является равномерно параболической в смысле Петровского. Построенная асимптотика содержит параболических погранслойных функций, описываемых “дополнительным интегралом вероятности”. . . . More less

Asan ÖMÜRALİEV | Ella ABILAYEVA

Proceedings Paper | 2017 | AIP Conference Proceedings1880 ( 1 )

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem when the limit operator has not range and with rapidly oscillating free term, its derivative of the phase vanishes at finite points. The vanishing of the first derivative of the phase of the free term induces transition layers. It is shown that the asymptotic solution of the problem contains parabolic, inner, corner and rapidly oscillating boundary-layer functions. Corner boundary-layer functions have two components: the first component is described by the product of parabolic boundary layer and boundary layer fu . . .nctions, which have a rapidly oscillating nature of the change, and the second component is described by the product of the inner and parabolic boundary layer functions More less

Asan ÖMÜRALİEV | Ella ABILAYEVA

Article | 2022 | MANAS Journal of Engineering (MJEN)10 ( 2 )

Asymptotic study of singularly perturbed differential equations of hyperbolic type has received relatively little attention from researchers. In this paper, the asymptotic solution of the singularly perturbed Cauchy problem for a hyperbolic system is constructed. In addition, the regularization method for singularly perturbed problems of S. A. Lomov is used for the first time for the asymptotic solution of a hyperbolic system. It is shown that this approach greatly simplifies the construction of the asymptotics of the solution for singularly perturbed differential equations of hyperbolic type.

Asan ÖMÜRALİEV

Article | 2019 | Differential Equations55 ( 6 )

The first boundary value problem is studied for an n-dimensional parabolic linear system of differential equations with a small parameter multiplying the spatial derivative. A complete regularized asymptotics of the solution is constructed for the case in which the system is uniformly Petrovskii parabolic. The asymptotics contains 2n parabolic boundary layer functions described by the complementary error function.

Asan ÖMÜRALİEV | Meerim İmaş Kızı

Article | 2017 | Differential Equations53 ( 12 )

The first boundary value problem for a multidimensional parabolic differential equation with a small parameter ε multiplying all derivatives is studied. A complete (i.e., of any order with respect to the parameter) regularized asymptotics of the solution is constructed, which contains a multidimensional boundary layer function that is bounded for x = (x 1, x 2) = 0 and tends to zero as ε → +0 for x ≠ 0. In addition, it contains corner boundary layer functions described by the product of a boundary layer function of the exponential type by a multidimensional parabolic boundary layer function

Elman HAZAR | Dağıstan ŞİMŞEK | Asan ÖMÜRALİEV | Burak OĞUL | Ella ABILAYEVA | Peyil Esengul Kızı

Article | 2015 | MANAS Journal of Engineering (MJEN)3 ( 2 )

In the present study, a boundary-value problem corresponding to forced vibration of an imperfectly bonded bi-layered plate-strip resting on a rigid foundation is considered. In the framework of three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modelling of considered problem is given. Then, the variational formulation of the problem considered is obtained in the framework of the principles of calculus of variation. The problem considered differs from the previous studies in the view of imperfect boundary conditions between the layers of the plate-stip and between the plate-strip and . . .the rigid foundation. - Keywords: Forced vibration, plate-strip, variational formulation More less

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

Article | 2021 | Differential Equations57 ( 1 )

We construct a regularized asymptotics of the solution of the first boundary value problem for a singularly perturbed two-dimensional differential equation of the parabolic type for the case in which the limit equation has a regular singularity. There arise power-law and corner boundary layers along with parabolic ones in such problems.

Asan ÖMÜRALİEV

Article | 2016 | Вестник Пермского университета. Серия: Математика. Механика. Информатика ( 2 )

Изучается система сингулярно возмущенных параболических уравнений, когда малый параметр находится как перед временной производной, так и перед пространственной производной, при этом предельный оператор имеет кратную нулевую точку спектра. В таких задачах возникают явления угловых погранслоев, описываемые произведением экспоненциальной и параболической погранслойных функций. В предположении, что предельный оператор является оператором простой структуры, построена регуляризо-ванная асимптотика решения, которая кроме угловых погранслойных функций содержит экспоненциальную и параболическую погранслойные функции. Построение асимптотики о . . .сновано на методе регуляризации для сингулярно возмущенных задач, разработанном С. А. Ломовым и адаптированном на сингулярно возмущенных параболических уравнениях с двумя вязкими границами одним из авторов.- Ключевые слова: сингулярно возмущенные параболические уравнения, регуляризованная асимптотика, экспоненциальные погранслои, параболические погранслои, singularly perturbed parabolic equations, regularized asymptotic behavior, exponential boundary layers, parabolic boundary layer More less