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Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Published online by Cambridge University Press:  15 April 2002

Slim Chaabane  and
Mohamed Jaoua
Slim Chaabane
Affiliation:
Faculté des Sciences de Sfax & ENIT-L A1. (slim.chaabane@fsm.rnu.tn)
Mohamed Jaoua
Affiliation:
ENIT-L A1, BP 37 1002 Tunis-Belvédère, Tunisie. (mohamed.jaoua@enit.rnu.tn)
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Abstract

This work deals with a non linear inverse problem of reconstructing an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction θ depends only on the state u0, and not on its Lagrangian derivative u1(θ).

Keywords

Geometrical inverse problemsidentificationSignorini type boundary conditionsunknown boundarydomaine derivativesKohn-Vogelius functionoptimal shape design.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 3 , May 2000 , pp. 707 - 722
Copyright
© EDP Sciences, SMAI, 2000

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