Asymptotic solution of a system of singularly-perturbed equations of elliptic type with an angular boundary layer

1981 ◽  
Vol 21 (3) ◽  
pp. 134-147
Author(s):  
V.F. Butuzov ◽  
Yu.P. Udodov
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Singularly Perturbed ◽  
Elliptic Type ◽  
Singularly Perturbed Equations ◽  
Angular Boundary

scholarly journals Singularly perturbed parabolic problem with oscillating initial condition

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1323-1327
Author(s):  
Asan Omuraliev ◽  
Ella Abylaeva
Keyword(s):  
Boundary Layer ◽  
Parabolic Problem ◽  
Singularly Perturbed ◽  
Initial Condition ◽  
Parabolic Boundary ◽  
Layer Function ◽  
Angular Boundary ◽  
Singularly Perturbed Parabolic Problem ◽  
Boundary Layer Function ◽  
Regularized Asymptotics

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 regularized asymptotics of the solution of the problem is constructed.

SINGULARLY PERTURBED PERIODIC PARABOLIC EQUATIONS WITH ALTERNATING BOUNDARY LAYER TYPE SOLUTIONS IN SPATIALLY TWO-DIMENSIONAL DOMAINS

2013 ◽  
Vol 11 (05) ◽  
pp. 1350029
Author(s):  
ADELAIDA B. VASIL'EVA ◽  
LEONID V. KALACHEV
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Parabolic Equations ◽  
The Other ◽  
Singularly Perturbed ◽  
Regular Part ◽  
Degenerate Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Spatial Domains

In this article, we continue the analysis of a class of singularly perturbed parabolic equations with alternating boundary layer type solutions. For such problems, the degenerate (reduced) equations obtained by setting a small parameter equal to zero correspond to algebraic equations that have several isolated roots. As time increases, solutions of these equations periodically go through two comparatively long lasting stages with fast transitions between these stages. During one of these stages, the solution outside the boundary layer (i.e. the regular part of the asymptotic solution) is close to one of the roots of the degenerate equation. During the other stage, the regular part of the asymptotic solution is close to the other root. Here we discuss some specific features of the solutions' behavior for such problems in certain two-dimensional spatial domains.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

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