Ginzburg-Landau dynamics with a time-dependent magnetic field

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