Partial Differential Equations
Magnetic Ginzburg–Landau functional with discontinuous constraint
[Une fonctionnelle de Ginzburg–Landau magnétique avec une contrainte discontinue]
Comptes Rendus. Mathématique, Tome 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.

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

1 Université Paris-Sud, département de mathématiques, bâtiment 425, 91405 Orsay cedex, France
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Kachmar, Ayman. Magnetic Ginzburg–Landau functional with discontinuous constraint. Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 297-300. doi : 10.1016/j.crma.2008.01.018. http://www.numdam.org/articles/10.1016/j.crma.2008.01.018/

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

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

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

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

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

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

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

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