Identification of cracks with non linear impedances

Mohamed Jaoua; Serge Nicaise; Luc Paquet

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 241-257
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Jaoua, Mohamed, Nicaise, Serge, and Paquet, Luc. "Identification of cracks with non linear impedances." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 241-257. <http://eudml.org/doc/194161>.

@article{Jaoua2010,
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. },
author = {Jaoua, Mohamed, Nicaise, Serge, Paquet, Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Inverse problems; cracks.; inverse problems; cracks; nonlinear impedance law; local Lipschitz stability; identifiability},
language = {eng},
month = {3},
number = {2},
pages = {241-257},
publisher = {EDP Sciences},
title = {Identification of cracks with non linear impedances},
url = {http://eudml.org/doc/194161},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Jaoua, Mohamed
AU - Nicaise, Serge
AU - Paquet, Luc
TI - Identification of cracks with non linear impedances
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 241
EP - 257
AB - 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.
LA - eng
KW - Inverse problems; cracks.; inverse problems; cracks; nonlinear impedance law; local Lipschitz stability; identifiability
UR - http://eudml.org/doc/194161
ER -

References

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  1. 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.  
  2. G. Alessandrini, E. Beretta and S. Vessella, Determining linear cracks by boundary measurements: Lipschitz stability. SIAM J. Math. Anal.27 (1996) 361-375.  
  3. G. Alessandrini and A. Diaz Valenzuela, Unique determination of multiple cracks by two measurements. SIAM J. Control Optim.34 (1996) 913-921.  
  4. G. Alessandrini and A. DiBenedetto, Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability. Indiana Univ. Math. J.46 (1997) 1-82.  
  5. S. Andrieux and A. Ben Abda, Identification of planar cracks by overdetermined boundary data: inversion formulae. Inverse Problems12 (1996) 553-563.  
  6. S. Andrieux, A. Ben Abda and M. Jaoua, On the inverse emerging plane crack problem. Math. Methods Appl. Sci.21 (1998) 895-907.  
  7. A. Ben Abda, H. Ben Ameur and M. Jaoua, A semi-explicit algorithm for the reconstruction of 3D planar cracks. Inverse Problems15 (1999) 67-78.  
  8. R. Bellout and A. Friedman, Identification problems in potential theory. Arch. Rational Mech. Anal.101 (1988) 143-160.  
  9. M. Bonnet, Boundary Integral Equation Methods for Solids and Fluids. Wiley, New York (1995).  
  10. K. Bryan and M. Vogelius, 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.  
  11. M. Dauge, Elliptic boundary value problems in corner domains. Smoothness and asymptotics of solutions. Springer Verlag, Berlin, Lecture Notes in Math.1341 (1988).  
  12. C. Dellacherie and P.-A. Meyer, Probabilité et potentiel. Hermann (1975).  
  13. P. Destuynder and M. Jaoua, Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile. Math. Methods Appl. Sci.3 (1981) 70-87.  
  14. 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).  
  15. A. Friedman and M. Vogelius, Determining cracks by boundary measurements. Indiana Univ. Math. J.38 (1989) 527-556.  
  16. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston (1985).  
  17. V.G. Maz'ya and B.A. Plamenevsky, On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Amer. Math. Soc. Transl. Ser. 2123 (1984) 57-88.  
  18. F. Murat and J. Simon, Quelques résultats sur le contrôle par un domaine géométrique. Preprint, Université de Paris VI (1974).  
  19. E.P. Stephan, Boundary integral equations for mixed boundary value problems, screen and transmission problems in 3 . Habilitationsschrift, TH Darmstadt, Germany (1984).  
  20. E.P. Stephan, Boundary integral equations for screen problems in 3 . Integral Equations Operator Theory10 (1987) 236-257.  
  21. V.S. Vladimirov, Equations of Mathematical Physics. Marcel Dekker, New York (1971).  

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