On the existence, regularity and large time behavior of a two-dimensional parabolic-elliptic eddy current problem
We consider a two-dimensional time-dependent eddy current model formulated as a parabolic-elliptic interface problem. Existence of solutions is established using Laplace transform techniques, potential theory and integral equations methods. Regularity results are shown, from which the existence of classical solutions follow. A large time behavior for the solution is established.