Free Access
Issue
ESAIM: M2AN
Volume 36, Number 6, November/December 2002
Page(s) 971 - 993
DOI https://doi.org/10.1051/m2an:2003001
Published online 15 January 2003
  1. C. Bolley and P. Del Castillo, Existence and uniqueness for the half-space Ginzburg-Landau model. Nonlinear Anal. 47/1 (2001) 135-146.
  2. C. Bolley and B. Helffer, Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak κ-limit. Rev. Math. Phys. 8 (1996) 43-83. [CrossRef] [MathSciNet]
  3. C. Bolley and B. Helffer, Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field. Part II. Nonlinear Stud. 3 (1996) 1-32. [MathSciNet]
  4. C. Bolley and B. Helffer, Proof of the De Gennes formula for the superheating field in the weak-κ limit. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 597-613. [CrossRef] [MathSciNet]
  5. C. Bolley and B. Helffer, Superheating in a semi-infinite film in the weak-κ limit: Numerical results and approximate models. ESAIM: M2AN 31 (1997) 121-165.
  6. C. Bolley and B. Helffer, Upper bound for the solution of the Ginzburg-Landau equations in a semi-infinite superconducting field and applications to the superheating field in the large κ regime. European J. Appl. Math. 8 (1997) 347-367. [MathSciNet]
  7. C. Bolley, F. Foucher and B. Helffer, Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. J. Math. Phys. 41 (2000) 7263-7289. [CrossRef] [MathSciNet]
  8. S. Chapman, Superheating field of type II superconductors. SIAM J. Appl. Math. 55 (1995) 1233-1258. [CrossRef] [MathSciNet]
  9. P. Del Castillo, Thèse de doctorat. Université Paris-Sud (2000).
  10. P. Del Castillo, Two terms in the lower bound for the superheating field in a semi-infinite film in the weak-κ limit. European J. Appl. Math. (2002).
  11. P.G. De Gennes, Superconductivity: Selected topics in solid state physics and theoretical Physics, in Proc. of 8th Latin american school of physics. Caracas (1966).
  12. V.L. Ginzburg, On the theory of superconductivity. Nuovo Cimento 2 (1955) 1234.
  13. V.L. Ginzburg, On the destruction and the onset of superconductivity in a magnetic field. Zh. Èksper. Teoret. Fiz. 34 (1958) 113-125; Transl. Soviet Phys. JETP 7 (1958) 78-87.
  14. Di Bartolo, T. Dorsey and J. Dolgert, Superheating fields of superconductors: Asymptotic analysis and numerical results. Phys. Rev. B 53 (1996); Erratum. Phys. Rev. B 56 (1997).
  15. W. Eckhaus, Matched asymptotic expansions and singular perturbations. North-Holland, Math. Studies 6 (1973).
  16. B. Helffer and F. Weissler, On a family of solutions of the second Painlevé equation related to superconductivity. European J. Appl. Math. 9 (1998) 223-243. [CrossRef] [MathSciNet]
  17. H. Parr, Superconductive superheating field for finite κ. Z. Phys. B 25 (1976) 359-361.
  18. M. van Dyke, Perturbation Methods in fluid mechanics. Academic Press, Stanford CA (1975).
  19. B. Rothberg-Bibby, H.J. Fink and D.S. McLachlan, First and second order phase transitions of moderately small superconductor in a magnetic field. North-Holland (1978).
  20. S. Kaplun, Fluid mechanics and singular perturbations. Academic Press (1967).

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