We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Mots-clés : inverse problems, cracks
@article{M2AN_2003__37_2_241_0, author = {Jaoua, Mohamed and Nicaise, Serge and Paquet, Luc}, title = {Identification of cracks with non linear impedances}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {241--257}, publisher = {EDP-Sciences}, volume = {37}, number = {2}, year = {2003}, doi = {10.1051/m2an:2003033}, mrnumber = {1991199}, zbl = {1029.35221}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2003033/} }
TY - JOUR AU - Jaoua, Mohamed AU - Nicaise, Serge AU - Paquet, Luc TI - Identification of cracks with non linear impedances JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 241 EP - 257 VL - 37 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003033/ DO - 10.1051/m2an:2003033 LA - en ID - M2AN_2003__37_2_241_0 ER -
%0 Journal Article %A Jaoua, Mohamed %A Nicaise, Serge %A Paquet, Luc %T Identification of cracks with non linear impedances %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 241-257 %V 37 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003033/ %R 10.1051/m2an:2003033 %G en %F M2AN_2003__37_2_241_0
Jaoua, Mohamed; Nicaise, Serge; Paquet, Luc. Identification of cracks with non linear impedances. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 241-257. doi : 10.1051/m2an:2003033. http://www.numdam.org/articles/10.1051/m2an:2003033/
[1] Stability for the crack determination problem, in Inverse problems in Mathematical Physics, L. Päıvaärinta and E. Somersalo Eds., Springer-Verlag, Berlin (1993) 1-8. | Zbl
,[2] Determining linear cracks by boundary measurements: Lipschitz stability. SIAM J. Math. Anal. 27 (1996) 361-375. | Zbl
, and ,[3] Unique determination of multiple cracks by two measurements. SIAM J. Control Optim. 34 (1996) 913-921. | Zbl
and ,[4] Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability. Indiana Univ. Math. J. 46 (1997) 1-82. | Zbl
and ,[5] Identification of planar cracks by overdetermined boundary data: inversion formulae. Inverse Problems 12 (1996) 553-563. | Zbl
and ,[6] On the inverse emerging plane crack problem. Math. Methods Appl. Sci. 21 (1998) 895-907. | Zbl
, and ,[7] A semi-explicit algorithm for the reconstruction of 3D planar cracks. Inverse Problems 15 (1999) 67-78. | Zbl
, and ,[8] Identification problems in potential theory. Arch. Rational Mech. Anal. 101 (1988) 143-160. | Zbl
and ,[9] Boundary Integral Equation Methods for Solids and Fluids. Wiley, New York (1995). | Zbl
,[10] A uniqueness result concerning the identification of a collection of cracks from finitely many electrostatic boundary measurements. SIAM J. Math. Anal. 23 (1992) 950-958. | Zbl
and ,[11] Elliptic boundary value problems in corner domains. Smoothness and asymptotics of solutions. Springer Verlag, Berlin, Lecture Notes in Math. 1341 (1988). | MR | Zbl
,[12] Probabilité et potentiel. Hermann (1975). | MR | Zbl
and ,[13] Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile. Math. Methods Appl. Sci. 3 (1981) 70-87. | Zbl
and ,[14] Étude de l'identifiabilité et de la stabilité d'une fissure présentant une résistivité de contact. DEA de Mathématiques Appliquées, ENIT, Tunis (1997).
,[15] Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (1989) 527-556. | Zbl
and ,[16] Elliptic problems in nonsmooth domains. Pitman, Boston (1985). | MR | Zbl
,[17] On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Amer. Math. Soc. Transl. Ser. 2 123 (1984) 57-88. | Zbl
and ,[18] Quelques résultats sur le contrôle par un domaine géométrique. Preprint, Université de Paris VI (1974). | MR
and ,[19] Boundary integral equations for mixed boundary value problems, screen and transmission problems in . Habilitationsschrift, TH Darmstadt, Germany (1984).
,[20] Boundary integral equations for screen problems in . Integral Equations Operator Theory 10 (1987) 236-257. | Zbl
,[21] Equations of Mathematical Physics. Marcel Dekker, New York (1971). | MR | Zbl
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