On a free-boundary problem modeling the action of a limiter on a plasma

Pages: 313 - 322, Issue Special, September 2007

 Abstract        Full Text (231.1K)              

J. I. Díaz - Dept. Matemática Aplicada. F. Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain (email)
J. F. Padial - Dpto. Matemática Aplicada, Fac. de Matemáticas, U. Politécnica de Madrid, 28040 Madrid, Spain (email)

Abstract: In this paper we prove the existence of weak solutions for a 2D free–boundary problems arising in the magnetic confinement of a plasma in a Stellarator device which includes the action of a limiter. The model can be expressed as an inverse thin obstacle problem in which the limiter plays the role of a thin obstacle for the plasma. The inverse nature of the problem comes from the fact that the associated Grad–Shafranov equation involves some unknown nonlinear terms which must be determined by the current–carrying Stellarator condition.

Keywords:  Inverse nonlinear elliptic problem, thin obstacle problem, relative rearrangement, Galerkin methods, free boundary problem,Current–carrying Stellarators.
Mathematics Subject Classification:  Primary: 35J85; Secondary: 35R30.

Received: September 2006;      Revised: February 2007;      Published: September 2007.