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An elliptic-parabolic equation with a nonlocal term for the transient regime of a plasma in a stellarator. (English) Zbl 1050.35151
Authors’ summary: The existence and the regularity of weak solutions of a nonlocal elliptic-parabolic free-boundary problem involving the notions of relative rearrangement and monotone rearrangement are proven. 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.
MSC:
35R35Free boundary problems for PDE
35M10PDE of mixed type
82D10Plasmas (statistical mechanics)
76X05Ionized gas flow in electromagnetic fields; plasmic flow
35D10Regularity of generalized solutions of PDE (MSC2000)