Periodic unfolding and homogenization for the Ginzburg-Landau Equation
| dc.creator | Sauvageot, Myrto | |
| dc.date | 2009-04-11 | |
| dc.date.accessioned | 2026-07-07T13:03:18Z | |
| dc.date.available | 2026-07-07T13:03:18Z | |
| dc.description | We investigate, on a bounded domain $Ω$ of $\R^2$ with fixed $S^1$-valued boundary condition $g$ of degree $d>0$, the asymptotic behaviour of solutions $u_{\varepsilon,δ}$ of a class of Ginzburg-Landau equations driven by two parameter : the usual Ginzburg-Landau parameter, denoted $\varepsilon$, and the scale parameter $δ$ of a geometry provided by a field of $2\times 2$ positive definite matrices $x\to A(\frac{x}δ)$. The field $\R^2\ni x\to A(x)$ is of class $W^{2,\infty}$ and periodic. We show, for a suitable choice of the $\varepsilon$'s depending on $δ$, the existence of a limit configuration $u_\infty\in H^1_g(Ω,S^1)$, which, out of a finite set of singular points, is a weak solution of the equation of $S^1$-valued harmonic functions for the geometry related to the usual homogenized matrix $A^0$. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1828 | |
| dc.identifier | http://arxiv.org/abs/0904.1828 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226752 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J25; 35J60 | |
| dc.title | Periodic unfolding and homogenization for the Ginzburg-Landau Equation | |
| dc.type | text |