| 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 | |
Expansion for the superheating field in a semi-infinite film in the weak-κ limit
UMR 8628 du CNRS,
Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France. pierre.castillo@math.u.psud.fr.
Received:
19
July
2001
Revised:
22
April
2002
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed
asymptotic matched solutions at order two for the half-space Ginzburg-Landau model,
in the weak-κ limit.
These authors deduced
a formal expansion for the superheating field in powers of 
up to
order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in
Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions
at all orders
leading to a complete expansion in powers of for the superheating field.
Mathematics Subject Classification: 34E05 / 34E10
Key words: Superconductivity / Ginzburg-Landau equation / critical field.
© EDP Sciences, SMAI, 2002
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