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

Amel Ben Abda , Slim Chaabane (1) , Fadi El Dabaghi (2) , Mohamed Jaoua (3)

1 GAMMA - Automatic mesh generation and adaptation methods
2 M3N - Multi-Models and Numerical Methods
3 MOSTRA - Numerical Modeling of Smart Materials and Adaptive Structures

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 $\beta > 0$.

Mots clés: GEOMETRICAL INVERSE PROBLEMS; IDENTIFICATION; SIGNORINI TYPE BOUNDARY CONDITIONS; UNKNOWN BOUNDARIES; IDENTIFIABILITY; LIPSCHITZ LOCAL STABILITY; DOMAIN DERIVATIVES; OPTIMAL SHAPE DESIGN

Domaines: Autre [cs.OH]

Amel Ben Abda, Slim Chaabane, Fadi El Dabaghi, Mohamed Jaoua. On a Non Linear Geometrical Inverse Problem of Signorini type : Identifiability and Stability. [Research Report] RR-3175, INRIA. 1997. ⟨inria-00077198⟩