Comptes Rendus
no. 5-6
Partial Differential Equations
Magnetic Ginzburg–Landau functional with discontinuous constraint
[Une fonctionnelle de Ginzburg–Landau magnétique avec une contrainte discontinue]

Présenté par : Jean-Michel Bony

Ayman Kachmar1
1 Université Paris-Sud, département de mathématiques, bâtiment 425, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 297-300.

Cette Note rend compte sur des résultats récents obtenus pour les minimiseurs d'une fonctionnelle de Ginzburg–Landau avec une contrainte discontinue. Ces résultats concernent le phénomène de chevillage (pinning) de vortex et les conditions aux limites pour des échantillons supraconducteurs inhomogènes.

This Note reports on results obtained for minimizers of a Ginzburg–Landau functional with discontinuous constraint. These results concern vortex-pinning and boundary conditions for inhomogeneous superconducting samples.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.01.018
Ayman Kachmar 1

1 Université Paris-Sud, département de mathématiques, bâtiment 425, 91405 Orsay cedex, France 
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Ayman Kachmar. Magnetic Ginzburg–Landau functional with discontinuous constraint. Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 297-300. doi : 10.1016/j.crma.2008.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.018/

[1] A. Aftalion; E. Sandier; S. Serfaty Pinning phenomena in the Ginzburg–Landau model of superconductivity, J. Math. Pures Appl., Volume 80 (2001), pp. 339-372

[2] S.J. Chapman; Q. Du; M.D. Gunzburger A Ginzburg Landau type model of superconducting/normal junctions including Josephson junctions, Eur. J. Appl. Math., Volume 6 (1996) no. 2, pp. 97-114

[3] S.J. Chapman; G. Richardson Vortex pinning by inhomogeneities in type II superconductors, Phys. D, Volume 108 (1997) no. 4, pp. 397-407

[4] P.G. de Gennes Superconductivity of Metals and Alloys, Benjamin, New York, 1966

[5] A. Kachmar, Magnetic vortices for a Ginzburg–Landau type energy with discontinuous constraint, Preprint

[6] A. Kachmar Limiting jump conditions for Josephson junctions in Ginzburg–Landau theory, Differential Integral Equations, Volume 21 (2008) no. 1–2, pp. 95-130

[7] A. Kachmar On the perfect superconducting solution for a generalized Ginzburg–Landau equation, Asymptotic Anal., Volume 54 (2007) no. 3–4, pp. 125-164

[8] A. Kachmar On the ground state energy for a magnetic Schrödinger operator and the effect of the de Gennes boundary condition, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 701-706

[9] L. Lassoued; P. Mironescu Ginzburg–Landau type energy with discontinuous constraint, J. Anal. Math., Volume 77 (1999), pp. 1-26

[10] E. Montevecchi; J.O. Indekeu Effects of confinement and surface enhancement on superconductivity, Phys. Rev. B, Volume 62 (2000), pp. 661-666

[11] E. Sandier; S. Serfaty Vortices for the Magnetic Ginzburg–Landau Model, Progress in Nonlinear Differential Equations and their Applications, vol. 70, Birkhaüser Boston, 2007

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