GINZBURG-LANDAU VORTICES - DYNAMICS, PINNING, AND HYSTERESIS

In this paper, we consider three problems related to the mathematical study of vortex phenomena in superconductivity based on the GL models. First, we study the long-time behavior of the solutions of the time-d ependent Ginzburg-Landau equations. Then we describe results concernin g the pinning effect of thin regions in a variable thickness thin film . Finally, we prove the existence of vortex-like solutions to the stea dy state Ginzburg-Landau equations and study the hysteresis phenomenon near the lower critical field.