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Reconnection of vortex with the boundary and finite time quenching. (English) Zbl 0910.35020

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.

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
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