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 language | English (US) |
|---|---|
| Pages (from-to) | 873-912 |
| Number of pages | 40 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 51 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 2019 |
All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics
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Cite this
Almog, Y., Berlyand, L., Golovaty, D., & Shafrir, I. (2019). Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents. SIAM Journal on Mathematical Analysis, 51(2), 873-912. https://doi.org/10.1137/17M1112285