The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem

Lia Bronsard; Barbara Stoth

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 3, page 371-397
  • ISSN: 0294-1449

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Bronsard, Lia, and Stoth, Barbara. "The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem." Annales de l'I.H.P. Analyse non linéaire 15.3 (1998): 371-397. <http://eudml.org/doc/78441>.

@article{Bronsard1998,
author = {Bronsard, Lia, Stoth, Barbara},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {time-dependent Ginzburg-Landau model; type I superconductivity; singular limit; one-phase Stefan problem; energy methods; monotonicity properties},
language = {eng},
number = {3},
pages = {371-397},
publisher = {Gauthier-Villars},
title = {The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem},
url = {http://eudml.org/doc/78441},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Bronsard, Lia
AU - Stoth, Barbara
TI - The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 3
SP - 371
EP - 397
LA - eng
KW - time-dependent Ginzburg-Landau model; type I superconductivity; singular limit; one-phase Stefan problem; energy methods; monotonicity properties
UR - http://eudml.org/doc/78441
ER -

References

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  2. [BS] L. Bronsard and B. Stoth, The Singular Limit of a Vector-Valued Reaction-Diffusion Process, preprint, 1995. MR1443865
  3. [C] J. Chapman, Asymptotic Analysis of the Ginzburg-Landau Model of Superconductivity: Reduction to a Free Boundary Model, preprint, 1992. 
  4. [CHO] J. Chapman, S.D. Howison and J.R. Ockendon, Macroscopic Models for Superconductivity, SIAM Rev., Vol. 34, 1992, pp. 529-560. Zbl0769.73068MR1193011
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  7. [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. Zbl0787.65091MR1156289
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  10. [GL] V.L. Ginzburg and L.D. Landau, On the theory of superconductivity, Soviet Phys., J.E.T.P., Vol. 20, 1950, pp. 1064. 
  11. [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. Zbl0088.45602
  12. [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. 
  13. [K] J.B. Keller, Propagation of a magnetic field into a superconductor, Phys. Rev., Vol. 111, 1958, pp. 1497. MR97945
  14. [L] J.L. Lions, Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1968. Zbl0189.40603MR259693
  15. [MO] W. Meissner and R. Ochsenfeld, Naturwissenschaften, Vol. 21, 1933, p. 787. 
  16. [M] A.M. Meirmanov, The Stefan Problem, De Gruyter Expositions in Mathematics, Berlin, 1992, New York. Zbl0751.35052MR1154310
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  18. [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. Zbl0876.35133MR1426212

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