Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents

Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this work, we consider a reduced Ginzburg-Landau model in which the magnetic field is neglected and the magnitude of the current density is significantly stronger than that considered in a recent work by the same authors. We prove the existence of a solution which can be obtained by solving a nonconvex minimization problem away from the boundary of the domain. Near the boundary, we show that this solution is essentially one-dimensional. We also establish some linear stability results for a simplified, one-dimensional version of the original problem.

Original languageEnglish (US)
Pages (from-to)873-912
Number of pages40
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number2
DOIs
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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