Ginzburg-Landau vortices, dynamics, pinning and hysteresis

Abstract. In this paper, we consider three problems related to the mathematical study of vortex phenomena in superconductivity based on the G{L models. First, we study the long-time behavior of the solutions of the time-dependent Ginzburg{Landau equations. Then we describe results concerning the pinning eect of thin regions in a variable thickness thin lm. Finally, we prove the existence of vortex-like solutions to the steady state Ginzburg{Landau equations and study the hysteresis phenomenon near the lower critical eld