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Identification of cracks with non linear impedances

Published online by Cambridge University Press:  15 November 2003

Mohamed Jaoua,
Serge Nicaise and
Luc Paquet
Mohamed Jaoua
Affiliation:
ENIT-LAMSIN, BP 37, 1002 Tunis-Bélvédère, Tunisia. Mohamed.Jaoua@enit.rnu.tn.
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, ISTV, MACS, 59313 Valenciennes Cedex 9, France. snicaise@univ-valenciennes.fr., Luc.Paquet@univ-valenciennes.fr.
Luc Paquet
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, ISTV, MACS, 59313 Valenciennes Cedex 9, France. snicaise@univ-valenciennes.fr., Luc.Paquet@univ-valenciennes.fr.
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Abstract

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.

Keywords

Inverse problemscracks.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003, pp. 241 - 257
Copyright
© EDP Sciences, SMAI, 2003

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References

G. Alessandrini, Stability for the crack determination problem, in Inverse problems in Mathematical Physics, L. Päivaärinta and E. Somersalo Eds., Springer-Verlag, Berlin (1993) 1-8.
Alessandrini, G., Beretta, E. and Vessella, S., Determining linear cracks by boundary measurements: Lipschitz stability. SIAM J. Math. Anal. 27 (1996) 361-375. CrossRef
Alessandrini, G. and Diaz Valenzuela, A., Unique determination of multiple cracks by two measurements. SIAM J. Control Optim. 34 (1996) 913-921. CrossRef
Alessandrini, G. and DiBenedetto, A., Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability. Indiana Univ. Math. J. 46 (1997) 1-82.
Andrieux, S. and Ben Abda, A., Identification of planar cracks by overdetermined boundary data: inversion formulae. Inverse Problems 12 (1996) 553-563. CrossRef
Andrieux, S., Ben Abda, A. and Jaoua, M., On the inverse emerging plane crack problem. Math. Methods Appl. Sci. 21 (1998) 895-907. 3.0.CO;2-1>CrossRef
Ben Abda, A., Ben Ameur, H. and Jaoua, M., A semi-explicit algorithm for the reconstruction of 3D planar cracks. Inverse Problems 15 (1999) 67-78. CrossRef
Bellout, R. and Friedman, A., Identification problems in potential theory. Arch. Rational Mech. Anal. 101 (1988) 143-160.
M. Bonnet, Boundary Integral Equation Methods for Solids and Fluids. Wiley, New York (1995).
Bryan, K. and Vogelius, M., 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. CrossRef
M. Dauge, Elliptic boundary value problems in corner domains. Smoothness and asymptotics of solutions. Springer Verlag, Berlin, Lecture Notes in Math. 1341 (1988).
C. Dellacherie and P.-A. Meyer, Probabilité et potentiel. Hermann (1975).
Destuynder, P. and Jaoua, M., Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile. Math. Methods Appl. Sci. 3 (1981) 70-87. CrossRef
R. Felfel, Étude de l'identifiabilité et de la stabilité d'une fissure présentant une résistivité de contact. DEA de Mathématiques Appliquées, ENIT, Tunis (1997).
Friedman, A. and Vogelius, M., Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (1989) 527-556. CrossRef
P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston (1985).
Maz'ya, V.G. and Plamenevsky, B.A., 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.
F. Murat and J. Simon, Quelques résultats sur le contrôle par un domaine géométrique. Preprint, Université de Paris VI (1974).
E.P. Stephan, Boundary integral equations for mixed boundary value problems, screen and transmission problems in ${\mathbb R}^3$ . Habilitationsschrift, TH Darmstadt, Germany (1984).
Stephan, E.P., Boundary integral equations for screen problems in ${\mathbb R}^3$ . Integral Equations Operator Theory 10 (1987) 236-257. CrossRef
V.S. Vladimirov, Equations of Mathematical Physics. Marcel Dekker, New York (1971).