Bean's critical-state model as the p → ∞ limit of an evolutionary p-Laplacian equation

The Bean critical-state model provides a description for the magnetization of type-II superconductors in a nonstationary external magnetic field. The model was first formulated for the simplest configuration of a cylindrical superconductor in a parallel field. Phenomenologically, the problem can be understood as a nonlinear eddy current problem. In accordance with the Faraday law of electromagnetic induction, the eddy currents in a conductor are driven by the electric fields induced by time variations of the magnetic flux. In an ordinary conductor, the vectors of the electric field and the current density are usually treated by the linear Ohm law.