Volume: 3, Issue: 1(2001)
pp. 1-14 DOI: 10.1142/S0219199701000275
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Abstract |
Full Text (PDF, 249KB)
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| Title: |
ON THE SYMMETRY AND UNIQUENESS OF SOLUTIONS
OF THE GINZBURG–LANDAU EQUATIONS FOR SMALL DOMAINS |
| Author(s): |
A. AFTALION
Laboratoire d'Analyse Numérique, B.C.187, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris cedex 05, France
E. N. DANCER
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
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| History: |
Received 12 September 1999
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| Abstract: |
In this paper, we study the Ginzburg–Landau equations for a two
dimensional domain which has small size. We prove that if the domain
is small, then the solution has no zero, that is no vortex. More
precisely, we show that the order parameter Ψ is almost constant.
Additionnally, we obtain that if the domain is a disc of small radius,
then any non normal solution is symmetric and unique. Then, in the
case of a slab, that is a one dimensional domain, we use the same
method to derive that solutions are symmetric. The proofs use a
priori estimates and the Poincaré inequality. |
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