Merle, Frank; Zaag, Hatem Reconnection of vortex with the boundary and finite time quenching. (English) Zbl 0910.35020 Nonlinearity 10, No. 6, 1497-1550 (1997). Author’s abstract: We construct a stable solution of the problem of vortex reconnection with the boundary in a superconductor under the planar approximation. That is a solution of \[ {\partial h\over \partial t} =\Delta h+e^{-h} H_0- {1\over h} \] (where \(H_0\) is the applied magnetic field assumed to be constant) such that \(h(0,t)\to 0\) as \(t\to T\). We give a precise description of the vortex near the reconnection point and time. We generalize the result to other quenching problems. Reviewer: C.Y.Chan (Lafayette) Cited in 2 ReviewsCited in 14 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35K57 Reaction-diffusion equations 35B45 A priori estimates in context of PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:stable solution; planar approximation PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Nonlinearity 10, No. 6, 1497--1550 (1997; Zbl 0910.35020) Full Text: DOI