Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs

Authors:
Jacob Rubinstein and Michelle Schatzman

Journal:
Trans. Amer. Math. Soc. **353** (2001), 4173-4187

MSC (2000):
Primary 82D55, 49S05, 94C15, 34B45

DOI:
https://doi.org/10.1090/S0002-9947-01-02804-5

Published electronically:
May 17, 2001

MathSciNet review:
1837226

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Abstract | References | Similar Articles | Additional Information

We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.

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Additional Information

**Jacob Rubinstein**

Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel

Email:
koby@leeor.technion.ac.il

**Michelle Schatzman**

Affiliation:
UMR 5585 CNRS MAPLY, Laboratoire de Mathématiques Appliquées de Lyon, Université Claude Bernard – Lyon 1, 69622 Villeurbanne Cedex, France

Email:
schatz@maply.univ-lyon1.fr

DOI:
https://doi.org/10.1090/S0002-9947-01-02804-5

Keywords:
Graph theory,
differential equations,
Ginzburg-Landau functional,
superconductivity

Received by editor(s):
March 28, 2000

Received by editor(s) in revised form:
August 14, 2000

Published electronically:
May 17, 2001

Additional Notes:
Supported by Israel Science Foundation, CNRS, and CNRS-MOSA binational agreement

Article copyright:
© Copyright 2001
American Mathematical Society