A singular nonlinear differential equation arising in the Homann flow
type: Item
instance of: scholarly article
title: A singular nonlinear differential equation arising in the Homann flow
zbMATH Open document ID: 0883.34021
author: Jun Yong Shin
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-02-23T00:00:00Z
review text: Existence and uniqueness of a positive solution of the singular nonlinear boundary value problem \[ yy''-\frac12(1-x^2)y'=0,\quad 0<x<1, \qquad y'(0)=-\frac12, \quad y(1)=0 \] is proved. First it is shown that the problem with \(y(1)=\frac1m\) instead of \(y(1)=0\) has a unique positive solution for each positive \(m\), and then it is shown that these solutions converge to a solution of the original problem if \(m\to\infty\).
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1053994
zbMATH Keywords: Homann flow
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: singular nonlinear boundary value problem
zbMATH Keywords: lower solution
zbMATH Keywords: upper solution
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5516
OpenAlex ID: W1987852532
cites work: Some singular, nonlinear differential equations arising in boundary layer theory
cites work: An analytical solution of a nonlinear, singular boundary value problem in the theory of viscous fluids
cites work: Q4283079
cites work: A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
cites work: A nonlinear boundary value problem
cites work: Existence and nonuniqueness of solutions of a singular nonlinear boundary-layer problem
cites work: On solutions of some singular, nonlinear differential equations arising in boundary layer theory
Wikidata QID: Q115395405
DOI: 10.1006/JMAA.1997.5516
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description: scientific article; zbMATH DE number 1053994