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Publisher : Springer ✕Subject Headings : parabolic boundary l ... ✕
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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 a two-dimensional singularly perturbed parabolic problem

Asan ÖMÜRALİEV

A regularized asymptotic expansion of the solution to a singularly perturbed two-dimensional parabolic problem in domains with boundaries containing corner points is constructed. The asymptotics of solutions to such problems contain ordinary boundary-layer functions, parabolic boundary-layer functions, and their products, which describe a corner boundary layer. - Keywords: singularly perturbed parabolic problems parabolic boundary layer regularized asymptotics

Article 2006 Fen Fakültesi Computational Mathematics and Mathematical Physics46 ( 8 ) 45 Views
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Singularly Perturbed System of Parabolic Equations in the Critical Case

Asan ÖMÜRALİEV

We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudar ...More

Article 2018 Fen Fakültesi Journal of Mathematical Sciences230 ( 5 ) 83 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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