no. 3
The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem
Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 3, pp. 371-397 
@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},
     pages = {371--397},
     year = {1998},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {3},
     mrnumber = {1629357},
     zbl = {0904.35083},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1998__15_3_371_0/}
}
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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) no. 3, pp. 371-397. https://www.numdam.org/item/AIHPC_1998__15_3_371_0/

[BCS] J. Bardee, L.N. Cooper and J.R. Schreiffer, Phys. Rev., Vol. 108, 1957, pp. 1175.

[BS] L. Bronsard and B. Stoth, The Singular Limit of a Vector-Valued Reaction-Diffusion Process, preprint, 1995. | MR

[C] J. Chapman, Asymptotic Analysis of the Ginzburg-Landau Model of Superconductivity: Reduction to a Free Boundary Model, preprint, 1992.

[CHO] J. Chapman, S.D. Howison and J.R. Ockendon, Macroscopic Models for Superconductivity, SIAM Rev., Vol. 34, 1992, pp. 529-560. | Zbl | MR

[CHL] Z. Chen, K.-H. Hoffman and J. Liang, On a Non-Stationary Ginzburg-Landau Superconductivity Model, Math. Meth. Appl. Scie., Vol. 16, 1993, pp. 855-875. | Zbl

[D] Q. Du, Global Existence and Uniqueness of Solutions of the Time-dependent Ginzburg-Landau Model for Superconductivity, Appl. Anal., Vol. 53, 1994, pp. 1-18. | Zbl | MR

[DGP] Q. Du, M.D. Gunzburger and J.S. Peterson, Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity, SIAM Rev., Vol. 34, 1992, pp. 54-81. | Zbl | MR

[ET] C.M. Elliott and Qi Tang, Existence Theorems for a Evolutionary Superconductivity Model, preprint, 1992.

[FH] A. Friedman and B. Hu, A free boundary problem arising in superconductor modeling, Asympt. Anal., Vol. 6, 1992, pp. 109-133. | Zbl | MR

[GL] V.L. Ginzburg and L.D. Landau, On the theory of superconductivity, Soviet Phys., J.E.T.P., Vol. 20, 1950, pp. 1064.

[G] L.P. Gor'Kov, Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity, Soviet Phys. J.E.T.P. Vol. 9, 1959, p. 1364. | Zbl

[GE] L.P. Gor'Kov and G.M. Éliashberg, 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] J.B. Keller, Propagation of a magnetic field into a superconductor, Phys. Rev., Vol. 111, 1958, pp. 1497. | MR

[L] J.L. Lions, Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1968. | Zbl | MR

[MO] W. Meissner and R. Ochsenfeld, Naturwissenschaften, Vol. 21, 1933, p. 787.

[M] A.M. Meirmanov, The Stefan Problem, De Gruyter Expositions in Mathematics, Berlin, 1992, New York. | Zbl | MR

[O] O.A. Oleinik, A method of solution for the general Stefan problem, Dokl. Akad. Nauk SSSR, Vol. 135, 1960, pp. 1054-1057. | MR

[S] B. Stoth, 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. | Zbl | MR