An elliptic–parabolic equation with a nonlocal term for the transient regime of a plasma in a Stellarator

We prove the existence and the regularity of weak solutions of a nonlocal elliptic–parabolic freeboundary problem involving the notions of relative rearrangement and monotone rearrangement. The problem arises in the study of the dynamics of a magnetically confined fusion plasma in a Stellarator device when the dimensional analysis on the characteristic times suggests to neglect the inertial acceleration in presence of a time dependent magnetic field.