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Transactions of the American Mathematical Society

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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:

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

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