On a family of solutions of the second Painlevé equation related to superconductivity

European Journal of Applied Mathematics

Volumn 9, Issue 3, 1998, Pages 223-243

  Helffer, Bernard ^a   Weissler, Fred B ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITÉ PARIS 13   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032387438     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792598003428     Document Type: Article

References (10)

1. CHAPMAN, S. J. (1995) Superheating field of type II superconductors. SIAM J. Appl. Math. 55(5), 1233-1258.
2. ITS, A. R. & NOVOKSHENOV, V. Y. (1986) The isomonodromic deformation method in the theory of the Painlevé equations. Lecture Notes in Mathematics 1191, Springer-Verlag.
3. LEVI, D. & WINTERNITZ, P. (eds.) (1990) Painlevé transcendents: their asymptotics and physical applications. NATO ASI Series, Series B: Physics. 278.
4. HASTINGS, S. P. & MCLEOD, J. B. (1980) A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rat. Mech. Anal. 73, 31-51.
5. BOLLEY, P. CAMUS, J. (1972) Sur une classe d'opérateurs elliptiques et dégénérés à une variable. J. Math. Pures et Appl., 51, 429-463.
6. BOLLEY, P., CAMUS, J. & HELFFER, B. (1976) Sur une classe d'opérateurs partiellement hypoelliptiques. J. Math. Pures et Appl., 55, 131-171.
7. 2)=0. Ann. IHP (Analyse non-linéaire) 11(4), 427-440.
8. BOLLEY, C. & HELFFER, B. (1996) Upper bounds for the solutions of the Ginzburg-Landau equations in a semi-infinite superconducting field and applications to the superheating field in the large κ regime. Euro. J. Appl. Math. (to appear).
9. VAN DYKE, M. (1964) Perturbation Methods in Mechanics. Academic Press.
10. DOLGERT, A. J., DI BARTOLO, S. J. & DORSEY, A. T. (1995) Superheating fields of superconductors: asymptotic analysis and numerical results. Preprint.