Bifurcation phenomena in singular free boundary value problems of ordinary differential equations
type: Item
instance of: scholarly article
title: Bifurcation phenomena in singular free boundary value problems of ordinary differential equations
zbMATH Open document ID: 0756.65111
DOI: 10.1016/0168-9274(92)90037-E
author: Wen Zhang
author: I. Gladwell
published in: Applied Numerical Mathematics
publication date: 1993-01-16T00:00:00Z
review text: The authors discuss the simple boundary value problem \(u'=(u-Rv)/(u^ 2- D^ 2-1)\), \(v'=(1-v)^ D\), \(v<1\); and \(=0\), \(v\geq 1\), with boundary conditions \(u(0)=D/2\), \(v(0)=0\), \(u(T)=Rv(T)\), \(u^ 2(T)=D^ 2+1\), where \(R\), \(D\) and \(T\) are unknown parameters. Depending on these parameters a singularity of \(u'\) at \(T\) may occur and cause some bifurcation effects. This partially explains bifurcation phenomena observed by the authors in a detonation problem. Numerical experiences are added.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L08
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 89538
zbMATH Keywords: singular free boundary value problems
zbMATH Keywords: bifurcation
zbMATH Keywords: Numerical experiences
reviewed by: Eckehard Pfeifer
describes a project that uses: nag
describes a project that uses: AUTO-86
describes a project that uses: NAG
MaRDI profile type: Publication
cites work: Q3994561
cites work: Q4861527
cites work: The Effect of Curvature on Detonation Speed
cites work: Bifurcation phenomena in a detonation problem
full work available at URL: 0168-9274(92)90037-e
OpenAlex ID: W1989134768
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description: scientific article; zbMATH DE number 89538