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A boundary value problem related to the Ginzburg-Landau model

Authors:

Anne Boutet de Monvel-Berthier Vladimir Georgescu Radu Purice

Institution:

(1) Equipe de Physique Mathématique et Géométrie, C.N.R.S., Université Paris VII, Tour 45-55, 5o-Etage, 2 Place Jussieu, F-75251 Paris Cedex 05, France;(2) Institut de Mathématique de l'Académie des Sciences de Roumanie, Bucarest, Roumanie

Abstract:

We analyze the Ginzburg-Landau equation for a superconductor in the case of a 2-dimensional model: a cylindrical conductor with a magnetic field parallel to the axis. This amounts to find the extrema of the free energy

$\mathcal{A}_\kappa = 1/2\int\limits_\Omega {\|(\nabla - iA]\Phi \|^2 + \|B_A \|^2 + \kappa /4(\|\Phi \|^2 - 1)^2 ]dx,}$

Keywords:
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