@article{AIHPC_1998__15_3_371_0,
author = {Bronsard, Lia and Stoth, Barbara},
title = {The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {15},
year = {1998},
pages = {371-397},
mrnumber = {1629357},
zbl = {0904.35083},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1998__15_3_371_0}
}
Bronsard, Lia; Stoth, Barbara. The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) pp. 371-397. http://gdmltest.u-ga.fr/item/AIHPC_1998__15_3_371_0/
[BCS] , and , Phys. Rev., Vol. 108, 1957, pp. 1175.
[BS] and , The Singular Limit of a Vector-Valued Reaction-Diffusion Process, preprint, 1995. | MR 1443865
[C] , Asymptotic Analysis of the Ginzburg-Landau Model of Superconductivity: Reduction to a Free Boundary Model, preprint, 1992.
[CHO] , and , Macroscopic Models for Superconductivity, SIAM Rev., Vol. 34, 1992, pp. 529-560. | MR 1193011 | Zbl 0769.73068
[CHL] , and , On a Non-Stationary Ginzburg-Landau Superconductivity Model, Math. Meth. Appl. Scie., Vol. 16, 1993, pp. 855-875. | Zbl 0817.35111
[D] , Global Existence and Uniqueness of Solutions of the Time-dependent Ginzburg-Landau Model for Superconductivity, Appl. Anal., Vol. 53, 1994, pp. 1-18. | MR 1379180 | Zbl 0843.35019
[DGP] , and , Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity, SIAM Rev., Vol. 34, 1992, pp. 54-81. | MR 1156289 | Zbl 0787.65091
[ET] and , Existence Theorems for a Evolutionary Superconductivity Model, preprint, 1992.
[FH] and , A free boundary problem arising in superconductor modeling, Asympt. Anal., Vol. 6, 1992, pp. 109-133. | MR 1193107 | Zbl 0851.35137
[GL] and , On the theory of superconductivity, Soviet Phys., J.E.T.P., Vol. 20, 1950, pp. 1064.
[G] , Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity, Soviet Phys. J.E.T.P. Vol. 9, 1959, p. 1364. | Zbl 0088.45602
[GE] and , Generalisation of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities, Soviet Phys. J.E.T.P., Vol. 27, 1968, pp. 328.
[K] , Propagation of a magnetic field into a superconductor, Phys. Rev., Vol. 111, 1958, pp. 1497. | MR 97945
[L] , Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1968. | MR 259693 | Zbl 0189.40603
[MO] and , Naturwissenschaften, Vol. 21, 1933, p. 787.
[M] , The Stefan Problem, De Gruyter Expositions in Mathematics, Berlin, 1992, New York. | MR 1154310 | Zbl 0751.35052
[O] , A method of solution for the general Stefan problem, Dokl. Akad. Nauk SSSR, Vol. 135, 1960, pp. 1054-1057. | MR 125341
[S] , A sharp interface limit of the phase field equations; Part I: 1-D, Part II: Axisymmetric, preprint, 1992, to appear in Europ. J. Appl. Math. | MR 1426212 | Zbl 0876.35133