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Peter Bates
Department of Mathematics,
Michigan State University
Nucleation of instability of the Meissner state of 3-dimensional superconductors
Monday 5th May 15:05-15:55pm,
Carslaw 273.
This talk concerns a nonlinear partial differential system in a
3-dimensional domain involving the operator curl^2, which is a
simplified model used to examine nucleation of instability of the
Meissner state of a superconductor as the applied magnetic field
reaches the superheating field. We derive a priori C^(2+alpha)
estimates for a weak solution H, the curl of the magnetic potential,
and determine the location of the maximal points of |curl H| which
correspond to the nucleation of instability of the Meissner state. We
show that, if the penetration length is small, the solution exhibits a
boundary layer. If the applied magnetic field is homogeneous, |curl H|
is maximal around the points on the boundary where the applied field
is tangential to the surface.
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