Calculus of Variations and Geometric Measure Theory

G. Crasta - A. Malusa

A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors.

created by malusa on 07 Mar 2008
modified on 15 Jul 2020


Published Paper

Inserted: 7 mar 2008
Last Updated: 15 jul 2020

Journal: Arch. Rational Mech. Anal.
Year: 2009


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.