Asymptotic Behavior of the Solutions of an Evolutionary Ginzburg-Landau Superconductivity Model

The asymptotic behaviour of the solutions of a non-stationary Ginzburg-Landau superconductivity model is discussed. Under suitable choices of gauge, it is proved that, as t tends to infinity, the ω-limit set of the solutions of the evolutionary superconductivity model consists of the solutions of the steady-state problem only. An example of non-convergence is also given for solutions under a particular choice of gauge.