Expansion for the superheating field in a semi-infinite film in the weak-κlimit

Pierre Del Castillo
2002 Mathematical Modelling and Numerical Analysis  
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 κ 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
more » ... powers of κ 1 2 for the superheating field. Mathematics Subject Classification. 34E05, 34E10.
doi:10.1051/m2an:2003001 fatcat:zphjqcezo5hi7djrmtiefqs2ue