We find local minimizers of the two-dimensional Ginzburg-Landau functional depending on a large parameter κ, which describe the behavior of a superconductor in a prescribed exterior magnetic field hex. We prove an estimate on the critical value Hc1 of hex(κ), corresponding to the first phase-transition in which vortices appear in the superconductor; and we locate these vortices.
|Original language||English (US)|
|Number of pages||42|
|Journal||Communications in Contemporary Mathematics|
|State||Published - May 1999|
ASJC Scopus subject areas
- Applied Mathematics