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Databases : Web of Science Core ... ✕Researcher : Asan ÖMÜRALİEV ✕
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Prof. Dr. Asan ÖMÜRALİEVFen Fakültesi
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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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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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A Singularly Perturbed System of Parabolic Equations

Asan ÖMÜRALİEV | Peyil Esengul Kızı

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.

Article 2021 Fen Fakültesi Lobachevskii Journal of Mathematics42 ( 15 ) 77 Views
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Singularly Perturbed Multidimensional Parabolic Equation with Rapidly Oscillating Free Term

Asan ÖMÜRALİEV | Ella ABILAYEVA

The regularized asymptotics of the solution of the first boundary-value problem for a two-dimensional differential equation of parabolic type is constructed in the case where the phase derivative vanishes at a single point. It is shown that angular and multidimensional boundary-layer functions appear in problems of this kind parallel with other types of boundary layers.

Article 2022 Fen Fakültesi Ukrainian Mathematical Journal73 ( 12 ) 80 Views
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Asymptotics of the Solution of a Parabolic Linear System with a Small Parameter

Asan ÖMÜRALİEV

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.

Article 2019 Fen Fakültesi Differential Equations55 ( 6 ) 75 Views
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Asymptotics of Solution to the Nonstationary Schrodinger Equation

Asan ÖMÜRALİEV | Peyil Esengul Kızı

The Cauchy problem with a rapidly oscillating initial condition for the homogeneous Schrodinger equation was studied in [5]. Continuing the research ideas of this work and [3], in this paper we construct the asymptotic solution to the following mixed problem for the nonstationary Schrodinger equation: L(h)u ih partial derivative(t)u + h(2)partial derivative(2)(x)u - b(x,t)u = f(x,t) (x,t) is an element of Omega = (0,1) x (0,t], u vertical bar(t=0) = g(x), u vertical bar(x=0) = u vertical bar(x=1) = 0 where h > 0 is a Planck constant, u = u(x,t,h). b(x,t), f (x,t) is an element of C-infinity ...More

Proceedings Paper 2019 Fen Fakültesi Filomat33 ( 5 ) 89 Views
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Singularly Perturbed Parabolic Problem with Oscillating Initial Condition

Asan ÖMÜRALİEV | Ella ABILAYEVA

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularize ...More

Proceedings Paper 2019 Fen Fakültesi Filomat33 ( 5 ) 139 Views
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Parabolic Problem with a Power-Law Boundary Layer

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

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.

Article 2021 Fen Fakültesi Differential Equations57 ( 1 ) 67 Views
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A System of Singularly Perturbed Parabolic Equations with a Power Boundary Layer

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

The 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 functions, and power boundary layer functions.

Article 2020 Fen Fakültesi Lobachevskii Journal of Mathematics41 ( 1 ) 65 Views
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Learners' Perceptions of Online Exams: A Comparative Study in Turkey and Kyrgyzstan

Rita İSMAİLOVA | Asan ÖMÜRALİEV | Gülşat MUHAMETJANOVA

As online learning is becoming very popular in formal educational settings and in individual development, online exams are starting to be recognized as one of the more efficient assessment methods. Online exams are effective in either blended or traditional forms of learning, and, when appropriately used, bring benefits to both learners and the learning process. However, learners

Article 2020 Mühendislik Fakültesi International Review of Research in Open and Distributed Learning (IRRODL)21 ( 3 ) 166 Views
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