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Found: 29 Piece 0.001 sn
Researcher : Asan ÖMÜRALİEV ✕
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Prof. Dr. Asan ÖMÜRALİEVFen Fakültesi
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Asymptotics of the solution of the hyperbolic system with a small parameter

Asan ÖMÜRALİEV | Ella ABILAYEVA

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.

Article 2022 Fen Fakültesi MANAS Journal of Engineering (MJEN)10 ( 2 ) 60 Views
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Ordinary differential equations with power boundary layers

Asan ÖMÜRALİEV | Ella ABILAYEVA

The regularized asymptotics of a solution of the Cauchy problem for systems of singularly perturbed ordinary differential equations is constructed. It is shown that a power boundary layer appears in such problems in addition to other boundary layers.

Article 2019 Fen Fakültesi Journal of Mathematical Sciences242 ( 3 ) 46 Views
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Regularization of the Singularly Perturbed Cauchy Problem for a Hyperbolic System

Asan ÖMÜRALİEV | Ella ABILAYEVA

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.

Article 2022 Fen Fakültesi Journal of Mathematical Sciences264 ( 4 ) 70 Views
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Regularized Asymptotics of the Solution of Systems of Parabolic Differential Equations

Asan ÖMÜRALİEV | Ella ABILAYEVA

The regularization method for singularly perturbed problems of S. A. Lomov is generalized to constructing the asymptotics of the solution of the first boundary value problem for systems of differential equations of parabolic type with a small parameter at all derivatives.It is shown that the asymptotics of the solution of the problem contains n exponential, 2n parabolic and 2n angle boundary layer functions.The exponential boundary layer function describes the boundary layer along t 0, the boundary layer along x 0 and x 1 is described by parabolic boundary layer functions. © 2022, University o ...More

Article 2022 Fen Fakültesi Filomat36 ( 16 ) 21 Views
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Asymptotics of the Solution of Parabolic Problems with Multipoint Stationary Phase

Asan ÖMÜRALİEV | Ella ABILAYEVA

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 parabo ...More

Proceedings Paper 2017 Fen Fakültesi AIP Conference Proceedings1880 ( 1 ) 78 Views
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Singularly Perturbed Parabolic Problems with Multidimensional Boundary Layers

Asan ÖMÜRALİEV | Meerim İmaş Kızı

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

Article 2017 Fen Fakültesi Differential Equations53 ( 12 ) 66 Views
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Сингулярно возмущённые параболические задачи с многомерными пограничными слоями

Asan ÖMÜRALİEV | Meerim İmaş Kızı

Изучается первая краевая задача для многомерного дифференциального уравнения параболического типа с малым параметром при всех производных. Построена полная, т.е. любого порядка по параметру регуляризованная асимптотика решения, которая содержит многомерную погранслойную функцию, ограниченную при и стремящуюся к нулю при если Кроме того, она содержит угловые погранслойные функции, описываемые произведением погранслойной функции экспоненциального типа и многомерной параболической погранслойной функции.

Article 2017 Fen Fakültesi Дифференциальные уравнения53 ( 12 ) 108 Views
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Сингулярно возмущенная система параболических уравнений в критическом случае

Asan ÖMÜRALİEV

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 погранс ...More

Article 2016 Fen Fakültesi Вестник Пермского университета. Серия: Математика. Механика. Информатика ( 2 ) 27 Views
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Variational Formulation Of A Boundary-value Problem Corresponding To Forced Vibration Of An Imperfectly Bonded Bi-layered Plate-strip Resting On A Rigid Foundation

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

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 pla ...More

Article 2015 Fen Fakültesi MANAS Journal of Engineering (MJEN)3 ( 2 ) 123 Views
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Асимптотика решения параболической задачи при отсутствии спектра предельного оператора = Asymptotics of the solution to a parabolic problem with the limit operator having no spectra

Asan ÖMÜRALİEV

Строится регуляризованная асимптотика решения сингулярно возмущенной двумерной параболической задачи, когда предельный оператор не имеет спектра. В отличие от скалярной задачи, асимптотика решения двумерной задачи дополнительно содержит угловые параболические пограничные функции, которые описываются произведением параболических пограничных функций.

Article 2012 Fen Fakültesi Журнал вычислительной математики и математической физики / Computational Mathematics and Mathematical Physics52 ( 7 ) 53 Views
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On the asymptotics of solution of one problem of optimal control of the small-parameter parabolic equation

Asan ÖMÜRALİEV | Ramiz RAFATOV

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.

Article 2011 Fen Fakültesi Automation and Remote Control72 ( 1 ) 56 Views
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Об асимптотике решения одной задачи оптимального управления параболическим уравнением с малым параметром = On the Asymptotics of the Solution of an Optimal Control Problem for a Parabolic Equation with Small Parameter

Asan ÖMÜRALİEV | Ramiz RAFATOV

Cтроится регуляризованная асимптотика решения задачи оптимальногоуправления для сингулярно возмущенной параболической задачи. Асимптотика решения такой задачи содержит параболические погранслойные функции, описываемые специальной функцией, называемой “дополнительным интегралом вероятности”.

Article 2011 Fen Fakültesi Автоматика и телемеханика / Automation and Remote Control ( 1 ) 145 Views
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