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inria-00077198, version 1

## On a Non Linear Geometrical Inverse Problem of Signorini type : Identifiability and Stability

Amel Ben Abda, Slim Chaabane a1, Fadi El Dabaghi 2, Mohamed Jaoua b3

N° RR-3175 (1997)

Abstract: This report deals with a non linear inverse problem of identification of unknown boundaries, on which the prescribed conditions are of Signorini type. We first prove an identifiability result, in both frameworks of steady state thermal and elastostatics testing. Local Lipschitz stability of the solutions with respect to the boundary measurements is also established, in case of unknown boundaries which are parts of ${\cal C}^{1,\beta}$ Jordan curves, with $\beta > 0$.

• a –  ENIT
• b –  Ecole Nationale dÍngénieurs de Tunis
• 1:  GAMMA (INRIA Rocquencourt)
• INRIA
• 2:  M3N (INRIA Rocquencourt)
• INRIA
• 3:  MOSTRA (INRIA Rocquencourt)
• INRIA
• Domain : Computer Science/Other
• Keywords : GEOMETRICAL INVERSE PROBLEMS / IDENTIFICATION / SIGNORINI TYPE BOUNDARY CONDITIONS / UNKNOWN BOUNDARIES / IDENTIFIABILITY / LIPSCHITZ LOCAL STABILITY / DOMAIN DERIVATIVES / OPTIMAL SHAPE DESIGN
• Internal note : RR-3175
• Comment : Projet MOSTRA – Projet M3N

• inria-00077198, version 1
• oai:hal.inria.fr:inria-00077198
• From:
• Submitted on: Monday, 29 May 2006 17:18:32
• Updated on: Tuesday, 24 April 2007 12:45:59