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 effect of thin regions in a variable thickness thin film. 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 field.