Expansion for the superheating field in a semi-infinite film in the weak-$\kappa$ limit
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, p. 971-993

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-$\kappa$ limit. These authors deduced a formal expansion for the superheating field in powers of ${\kappa }^{\frac{1}{2}}$ 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 ${\kappa }^{\frac{1}{2}}$ for the superheating field.

DOI : https://doi.org/10.1051/m2an:2003001
Classification:  34E05,  34E10
Keywords: superconductivity, Ginzburg-Landau equation, critical field
@article{M2AN_2002__36_6_971_0,
author = {Castillo, Pierre Del},
title = {Expansion for the superheating field in a semi-infinite film in the weak-$\kappa$ limit},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
pages = {971-993},
doi = {10.1051/m2an:2003001},
zbl = {1037.34046},
mrnumber = {1958654},
language = {en},
url = {http://www.numdam.org/item/M2AN_2002__36_6_971_0}
}

Castillo, Pierre Del. Expansion for the superheating field in a semi-infinite film in the weak-$\kappa$ limit. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, pp. 971-993. doi : 10.1051/m2an:2003001. http://www.numdam.org/item/M2AN_2002__36_6_971_0/

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