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A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.
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Chapman et al. (1996) studied this question.
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