Proof of the De Gennes formula for the superheating field in the weak κ limit

Catherine Bolley; Bernard Helffer

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 5, page 597-613
  • ISSN: 0294-1449

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Bolley, Catherine, and Helffer, Bernard. "Proof of the De Gennes formula for the superheating field in the weak κ limit." Annales de l'I.H.P. Analyse non linéaire 14.5 (1997): 597-613. <http://eudml.org/doc/78422>.

@article{Bolley1997,
author = {Bolley, Catherine, Helffer, Bernard},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau system},
language = {eng},
number = {5},
pages = {597-613},
publisher = {Gauthier-Villars},
title = {Proof of the De Gennes formula for the superheating field in the weak κ limit},
url = {http://eudml.org/doc/78422},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Bolley, Catherine
AU - Helffer, Bernard
TI - Proof of the De Gennes formula for the superheating field in the weak κ limit
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 5
SP - 597
EP - 613
LA - eng
KW - Ginzburg-Landau system
UR - http://eudml.org/doc/78422
ER -

References

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  1. [1] C. Bolley and B. Helffer, Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field, Nonlinear Studies, Part I: Vol. 3, n° 1, 1996, pp. 1-29, Part II: Vol. 3, n° 2, 1996, pp. 1-32. Zbl0857.34006MR1396033
  2. [2] C. Bolley and B. Helffer, Sur les asymptotiques des champs critiques pour l'équation de Ginzburg-Landau. Séminaire Equations aux dérivées partielles de l'Ecole Polytechnique, November 1993. Zbl0877.35120
  3. [3] C. Bolley and B. Helffer, Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak κ-limit, Reviews in Math. Physics, Vol. 8, n° 1, 1996, pp. 43-83. Zbl0864.35097MR1372515
  4. [4] C. Bolley and B. Helffer, Superheating in a film in the weak κ limit: numerical results and approximate models, Dec. 1994 (Part I to appear in M2 AN). Zbl0868.65087
  5. [5] C. Bolley and B. Helffer, In preparation. 
  6. [6] S.J. Chapman, Asymptotic analysis of the Ginzburg-Landau model of superconductivity: reduction to a free boundary model, Preprint, 1992. Zbl0842.35120MR1359498
  7. [7] V.P. Galaiko, Superheating critical field for superconductors of the first kind, Soviet Physics JETP, Vol. 27, n° 1, July 1968. 
  8. [8] P.G. De Gennes, Superconductivity, selected topics in solid state physics and theoretical Physics, Proc. of 8th Latin american school of physics, Caracas, 1966. 
  9. [9] V.L. Ginzburg, On the theory of superconductivity, Nuovo Cimento, Vol. 2, 1955, p. 1234. Zbl0067.23504
  10. [10] V.L. Ginzburg, On the destruction and the onset of superconductivity in a magnetic field, Soviet Physics JETP, Vol. 7, 1958, p. 78. Zbl0099.44703
  11. [11] V.L. Ginzburg and L.D. Landau, On the theory of superconductivity, Zh. Eksperim. i teor. Fiz., Vol. 20, 1950, pp. 1064-1082. English translation Men of Physics, L. D. LANDAU, I, Ed. by D. TerHaar, Pergamonoxford, 1965, pp. 138-167. 
  12. [12] S.P. Hastings, M.K. Kwong and W.C. Troy, The existence of multiple solutions for a Ginzburg-Landau type model of superconductivity, Preprint May 1995. Zbl0880.34023MR1426209
  13. [13] D. Saint James and P.G. De Gennes, Onset of superconductivity in decreasing fields, Phys. Lett., Vol. 7, 1963, p. 306. 
  14. [14] D. Saint James, G. Sarma and E.J. Thomas, Type II Superconductivity, Pergamon Press, 1969. 
  15. [15] H. Parr, Superconductive superheating field for finite κ, Z. Physik, Vol. B25, 1976, pp. 359-361. 

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