# A branched transport limit of the Ginzburg-Landau functional

created by goldman on 05 Apr 2017

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Submitted Paper

Inserted: 5 apr 2017
Last Updated: 5 apr 2017

Year: 2017

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.