Reconnection of vortex with the boundary and finite time quenching

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 derivative h/partial derivative T = Delta h + e(-h) H-0 - 1/h such that h(0, t) --> 0 as t --> T. We give a precise description of the vortex near the reconnection point and time. We generalize the result to other quenching problems.