On solutions of some singular, nonlinear differential equations arising in boundary layer theory
type: Item
instance of: scholarly article
title: On solutions of some singular, nonlinear differential equations arising in boundary layer theory
zbMATH Open document ID: 0729.35103
DOI: 10.1016/0022-247X(91)90015-R
author: K. Vajrevelu
author: Edy Soewono
author: Ram N. Mohapatra
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The author considers the problem \[ g(x)g''(x)+h(x)=0,\quad k<x<1,\quad g'(k)=C,\quad g(1)=0 \] which is the Crocco variable formulation of a differential equation arising in boundary layer theory with suction/injection. The function h is continuous, positive, and \(\lim_{x\to \infty}h(x)/x>0\). The solution is obtained as the solution of the problem with the boundary condition \(g(1)=0\) replaced by the initial condition \(g(k)=\alpha\) for an appropriate value of \(\alpha\). The analyticity of the solution, and some estimates of the initial value \(\alpha\) and the maximum point of the solution are also established.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4204977
zbMATH Keywords: shear stress
zbMATH Keywords: tangential velocity
zbMATH Keywords: flow
zbMATH Keywords: semi-infinite flat plate
zbMATH Keywords: uniform stream
zbMATH Keywords: boundary layer
reviewed by: Hiroki Tanabe
MaRDI profile type: Publication
cites work: On the differential equations of the simplest boundary-layer problems
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cites work: Q3873786
cites work: Q5727762
full work available at URL: 0022-247x(91)90015-r
OpenAlex ID: W1987091670
description: scientific article; zbMATH DE number 4204977