Bifurcation phenomena in singular free boundary value problems of ordinary differential equations (Q1196762)

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.