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The Ginzburg–Landau equations in a semi-infinite superconducting film in the large κ limit

Published online by Cambridge University Press:  01 August 1997

CATHERINE BOLLEY
Affiliation:
Ecole Centrale de Nantes, 1, rue de la Noë, F-44072 Nantes Cedex 03, France
BERNARD HELFFER
Affiliation:
Département de Mathématiques, Université Paris-Sud, F-91405 Orsay, France

Abstract

Following our preceding papers [1, 2] concerning semi-infinite superconducting films, we consider new a priori estimates on the exterior magnetic field h=A′(0), when (f, A) is a solution of the corresponding Ginzburg–Landau system. The main new results concern the limit as κ→∞, but we prove also the existence of a finite superheating field. We also discuss recent results [3] concerning the superheating field in the large κ limit, and show how to relate these formal solutions to suitable subsolutions and supersolutions giving the existence of a solution for h<1/√2 and κ large enough. We also analyse the same problem by variational techniques and get the existence of a locally stable solution for h<1/√2 and any κ>0.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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