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Sergio Conti; Michael Goldman; Felix Otto; Sylvia Serfaty
A branched transport limit of the Ginzburg-Landau functional
(Dérivation d’une fonctionnelle de type transport branché à partir du modèle de Ginzburg-Landau)
Journal de l'École polytechnique — Mathématiques, 5 (2018), p. 317-375, doi: 10.5802/jep.72
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Class. Math.: 35Q56, 49S05, 82D55, 49J10, 49S05
Keywords: Gamma convergence, Ginzburg-Landau, branched transportation, pattern formation, type-I superconductors

Résumé - Abstract

We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via $\Gamma $-convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.

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