@article{9698ed561a064f75bab5e18c67580a7a,
title = "Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents",
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.",
author = "Yaniv Almog and Leonid Berlyand and Dmitry Golovaty and Itai Shafrir",
note = "Funding Information: \ast Received by the editors January 19, 2017; accepted for publication (in revised form) January 29, 2019; published electronically March 28, 2019. http://www.siam.org/journals/sima/51-2/M111228.html Funding: This work was partially supported by BSF grant 2010194. The first author's research was partially supported by NSF grant DMS-1613471. The second author's research was partially supported by NSF grant DMS-1405769. \dagger Department of Mathematics, Ort Braude College, Carmiel 21610, Israel (yalmog64@gmail.com). \ddagger Department of Mathematics, Penn State University, University Park, PA 16802 (berlyand@math. psu.edu). \S Department of Mathematics, University of Akron, Akron, OH 44325 (dgolovaty@gmail.com). \P Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel (shafrir@math.technion.ac.il). Funding Information: This work was partially supported by BSF grant 2010194. The first author's research was partially supported by NSF grant DMS-1613471. The second author's research was partially supported by NSF grant DMS-1405769. Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
doi = "10.1137/17M1112285",
language = "English (US)",
volume = "51",
pages = "873--912",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}