On a double boundary layer in a nonlinear boundary value problem
type: Item
instance of: scholarly article
title: On a double boundary layer in a nonlinear boundary value problem
zbMATH Open document ID: 1380.34088
DOI: 10.1134/S0081543817050145
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2017-10-27T00:00:00Z
review text: In this paper, the authors analyze the Dirichlet problem for the singularly perturbed second-order ordinary differential equation \[ \varepsilon^2 u_{xx}=u^2+\mu\left[ K(x,\mu)u+F(u,\varepsilon u_x,x,\mu)\right],\;0< x < L,\;0<\varepsilon\ll 1, \] \[ u(0)=\alpha(\mu),\;u(L)=\beta(\mu), \] where \(\mu=\varepsilon^{1/2}\) or \(\mu=\varepsilon,\) and \(K, F,\) \(\alpha\) and \(\beta\) are smooth functions in all variables. Using the asymptotic expansion techniques, the authors construct in the form of boundary layer expansion the formal (asymptotic) solution for the problem under consideration which provides its approximation for \(\varepsilon\rightarrow 0^+\) on the interval \([0,L]\).
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6798891
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary layer
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: matching method
author: Svetlana A. Kordyukova
author: L. A. Kalyakin
MaRDI profile type: Publication
cites work: Q3259838
cites work: Q4023364
cites work: Q4002771
cites work: The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point
cites work: Structure of boundary layers in singular problems
cites work: Q4761639
cites work: On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation
cites work: Singularly perturbed boundary value problems with a power-law boundary layer
cites work: Two-point boundary value problem for a singularly perturbed equation with a reduced equation having multiple roots
full work available at URL: s0081543817050145
OpenAlex ID: W2751069771
description: scientific article; zbMATH DE number 6798891