GINZBURG-LANDAU DYNAMICS WITH A TIME-DEPENDENT MAGNETIC-FIELD

The time-dependent Ginzburg-Landau equations of superconductivity defi ne a dynamical process when the applied magnetic field varies with tim e. Sufficient conditions (in terms of the time rate of change of the a pplied field) are given that, if satisfied, guarantee that this dynami cal process is asymptotically autonomous. As time goes to infinity, th e dynamical process asymptotically approaches a dynamical system whose attractor coincides with the omega-limit set of the dynamical process .