Inserted: 7 mar 2008
Last Updated: 15 jul 2020
Journal: Arch. Rational Mech. Anal.
We consider the Bean's critical state model for anisotropic superconductors. A variational problem solved by the quasi--static evolution of the internal magnetic field is obtained as the $\Gamma$-limit of functionals arising from the Maxwell's equations combined with a power law for the dissipation. Moreover, the quasi--static approximation of the internal electric field is recovered, using a first order necessary condition.
If the sample is a long cylinder subjected to an axial uniform external field, the macroscopic electrodynamics is explicitly determined.