On the periodic behavior of solutions to a diffusion problem describing currents in a high-temperature superconductor

We study the large time behavior of solutions to a model describing the current flow in a type-II superconducting wire subject to a periodic transport current and a transverse applied magnetic field. The model is given as an initial value problem for an elliptic-degenerate parabolic equation on R2. We show that the current distributions are asymptotically periodic in time as t→∞.