We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high k, placed in an applied magnetic field hex, when hex is of the order of the ＂first critical field＂, i.e. of the order of ｜lnε｜. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.
In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.
