Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-30T15:45:50.886Z Has data issue: false hasContentIssue false
  • English
  • Français

On the global bifurcation diagram for the one-dimensional Ginzburg–Landau model of superconductivity

Published online by Cambridge University Press:  01 June 2000

E. N. DANCER  and
S. P. HASTINGS
E. N. DANCER
Affiliation:
Department of Mathematics, University of Sydney, NSW 2006, Australia
S. P. HASTINGS
Affiliation:
Department of Mathematics, University of Pittsburgh, PA 15260, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Some new global results are given about solutions to the boundary value problem for the Euler–Lagrange equations for the Ginzburg–Landau model of a one-dimensional superconductor. The main advance is a proof that in some parameter range there is a branch of asymmetric solutions connecting the branch of symmetric solutions to the normal state. Also, simplified proofs are presented for some local bifurcation results of Bolley and Helffer. These proofs require no detailed asymptotics for solution of the linear equations. Finally, an error in Odeh's work on this problem is discussed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 3 , June 2000 , pp. 271 - 291
Copyright
2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)