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Analysis of a mean field model of superconducting vortices

Published online by Cambridge University Press:  01 August 1999

R. SCHÄTZLE  and
V. STYLES
R. SCHÄTZLE
Affiliation:
Mathematisches Institut der Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, D-79104 Freiburg, Germany (e-mail: schaetz@mathematik.uni-freiburg.de)
V. STYLES
Affiliation:
Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH, UK (e-mail: mmpb2@solx1.central.sussex.ac.uk)
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Abstract

We study a mean-field model of superconducting vortices in one and two dimensions. The existence of a weak solution and a steady-state solution of the model are proved. A special case of the steady-state problem is shown to be of the form of a free boundary problem. The solutions of this free boundary problem are investigated. It is also shown that the weak solution of the one-dimensional model is unique and satisfies an entropy inequality.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 4 , August 1999 , pp. 319 - 352
Copyright
1999 Cambridge University Press

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