On a Ginzburg-Landau type energy with discontinuous constraint for high values of applied field

Abstract

In the presence of applied magnetic fields H such that | lnɛ| ≪ H ≪ $\tfrac{1}{{\varepsilon ^2 }}$, the author evaluates the minimal Ginzburg-Landau energy with discontinuous constraint. Its expression is analogous to the work of Sandier and Serfaty.

Keywords

Ginzburg-Landau functional / Mixed phase / Discontinuous constraint

References

[1] Aydi H., Kachmar A.. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint, II. Comm. Pure. Appl. Anal., 2009, 8(3): 977-998

[2] Chapman S. J., Du Q., Gunzburger M. D.. A Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctions. European J. Appl. Math., 1996, 6: 97-114

[3] Giorgi T.. Superconductors surrounded by normal materials. Proc. Roy. Soc. Edinburgh Sec. A, 2005, 135: 331-356

[4] Kachmar A.. Magnetic Ginzburg-Landau functional with disconinuous constraint. C. R. Math. Acad. Sci. Paris, 2008, 346: 297-300

[5] Kachmar, A., Magnetic vortices for a Ginzburg-Landau type energy with disconinuous constraint, ESAIM: COCV, accepted.

[6] Kachmar A.. On the perfect superconducting solution for a generalized Ginzburg-Landau equation. Asymptot. Anal., 2007, 54: 125-164

[7] Lassoued L., Mironescu P.. Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math., 1999, 77: 1-26

[8] Rubinstein J.. Delfour M.. Six Lectures on Superconductivity, Boundaries, Interfaces and Transitions, 1998, Providence, RI: A. M. S. 163-184

[9] Sandier E., Serfaty S.. On the energy of type-II superconductors in the mixed phaseA. Review. Math. Phys, 2000, 12(9): 1219-1257

[10] Sandier E., Serfaty S.. A rigorous derivation of a free-boundary problem arising in superconductivity. Annales Scientifiques de l’ENS, 2000, 33: 561-592

[11] Sandier E., Serfaty S.. Vortices for the magnetic Ginzburg-Landau model, 2007, Boston: Birkhäuser