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2011, 2011(Special): 1176-1185. doi: 10.3934/proc.2011.2011.1176

Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion

J. F. Padial 1,

1. 

Dpto. Matemática Aplicada, Fac. de Matemáticas, U. Politécnica de Madrid, 28040 Madrid, Spain

Received  August 2010 Revised  July 2011 Published  October 2011

We consider an inverse 2D free-boundary elliptic-parabolic problem, modeling the transient regime of a magnetically con ned plasma in a non ideal Stellarator device. 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. One of the main diculties for the mathematical approach is due to the fact that these nonlinear terms are neither a monotone function and are nor a Lipschitz function either. Nevertheless, we can introduce an auxiliary problem for which the solution of our original problem is a supersolution. On the other hand, we can to obtain a subsolution for this new problem. Finally, by applying the comparison principle for quasi-linear problems, we obtain some appropriate estimates on the location and size of the plasma region.
Keywords: Current-carrying Stellarators, free boundary problem, relative rearrangement, Inverse nonlinear elliptic-parabolic problem, location of free boundary.
Mathematics Subject Classification: Primary: 35J85; Secondary: 35R30.
Citation: J. F. Padial. Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion. Conference Publications, 2011, 2011 (Special) : 1176-1185. doi: 10.3934/proc.2011.2011.1176
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