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Some inverse problems around the tokamak Tore Supra. (English) Zbl 1267.30107

Summary: We consider two inverse problems related to the tokamak Tore Supra through the study of the magnetostatic equation for the poloidal flux. The first one deals with the Cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary, namely the limiter, from available overdetermined data on the outer boundary. Using tools from complex analysis and properties of genereralized Hardy spaces, we establish stability and existence properties. Secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization. Again results about existence and optimality are provided. They give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from Tore Supra.

MSC:

30H10 Hardy spaces
49J20 Existence theories for optimal control problems involving partial differential equations
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
30H05 Spaces of bounded analytic functions of one complex variable
42A50 Conjugate functions, conjugate series, singular integrals
35N05 Overdetermined systems of PDEs with constant coefficients
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