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The problem of detecting corrosion by an electric measurement revisited
1. | Institut Élie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine-Metz, Boulevard des Aiguillettes, BP 70239, 54506 Vandoeuvre les Nancy cedex, Ile du Saulcy, 57045 Metz cedex 01, France |
2. | Faculté des Sciences de Bizerte, Département des Mathématiques, 7021 Jarzouna Bizerte, Tunisia |
References:
[1] |
G. Alessandrini, L. Del Piero and L. Rondi, Stable determination of corrosion by a single electrostatic boundary measurement, Inverse problems, 19 (2003), 973-984.
doi: 10.1088/0266-5611/19/4/312. |
[2] |
G. Alessandrini, E. Sincich and S. Vessella, Stable determination of surface impedance on a rough obstacle by far field data, Inverse Problems and Imaging, 7 (2013), 341-351.
doi: 10.3934/ipi.2013.7.341. |
[3] |
M. Bellassoued, M. Choulli and A. Jbalia, Stability of the determination of the surface impedance of an obstacle from the scattering amplitude, Math. Methods Appl. Sci., 36 (2013), 2429-2448.
doi: 10.1002/mma.2762. |
[4] |
M. Bellassoued, J. Cheng and M. Choulli, Stability estimate for an inverse boundary coefficient problem in thermal imaging, J. Math Anal. Appl., 343 (2008), 328-336.
doi: 10.1016/j.jmaa.2008.01.066. |
[5] |
L. Bourgeois, About stability and regularization of ill-posed elliptic Cauchy problems: the case of $C^{1,1}$ domains, Math. Model. Numer. Anal., 44 (2010), 715-735.
doi: 10.1051/m2an/2010016. |
[6] |
S. Chaabane, I. Fellah, M. Jaoua and J. Leblond, Logarithmic stability estimates for a Robin coefficient in two-dimensional Laplace inverse problems, Inverse Problems, 20 (2004), 47-59.
doi: 10.1088/0266-5611/20/1/003. |
[7] |
S. Chaabane and M. Jaoua, Identification of Robin coefficients by the means of boundary measurements, Inverse Problems, 15 (1999), 1425-1438.
doi: 10.1088/0266-5611/15/6/303. |
[8] |
J. Cheng, M. Choulli and J. Lin, Stable determination of a boundary coefficient in an elliptic equation, Math. Models Methods Appl. Sci., 18 (2008), 107-123.
doi: 10.1142/S0218202508002620. |
[9] |
J. Cheng, M. Choulli and X. Yang, An iterative BEM for the inverse problem of detecting corrosion in a pipe, Numer. Math. J. Chinese Univ., 14 (2005), 252-266. |
[10] |
M. Choulli, Stability estimates for an inverse elliptic problem, J. Inverse Ill-Posed Probl., 10 (2002), 601-610.
doi: 10.1515/jiip.2002.10.6.601. |
[11] |
M. Choulli, An inverse problem in corrosion detection: Stability estimates, J. Inverse Ill-Posed Probl., 12 (2004), 349-367.
doi: 10.1515/1569394042248247. |
[12] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques, SMAI-Springer, Berlin, 2009.
doi: 10.1007/978-3-642-02460-3. |
[13] |
M. Choulli and F. Triki, New stability estimates for the inverse medium problem with internal data, SIAM J. Math. Anal., 47 (2015), 1778-1799.
doi: 10.1137/140988577. |
[14] |
M. Choulli, Applications of elliptic Carleman inequalities,, to appear in BCAM SpringerBriefs., ().
|
[15] |
D. Fasino and G. Inglese, An inverse Robin problem for Laplace's equation: Theoretical and numerical methods}, Inverse Problems, 15 (1999), 41-48.
doi: 10.1088/0266-5611/15/1/008. |
[16] |
G. Inglese, An inverse problem in corrosion detection, Inverse Problems, 13 (1997), 977-994.
doi: 10.1088/0266-5611/13/4/006. |
[17] |
E. Sincich, Stable determination of the surface impedance of an obstacle by far field measurements, SIAM J. Math. Anal., 38 (2006), 434-451.
doi: 10.1137/050631513. |
[18] |
E. Sincich, Lipschitz stability for the inverse Robin problem, Inverse Problems, 23 (2007), 1311-1326.
doi: 10.1088/0266-5611/23/3/027. |
[19] |
E. Sincich, Smoothness dependent stability in corrosion detection, J. Math. Anal. Appl., 426 (2015), 364-379.
doi: 10.1016/j.jmaa.2014.10.036. |
show all references
References:
[1] |
G. Alessandrini, L. Del Piero and L. Rondi, Stable determination of corrosion by a single electrostatic boundary measurement, Inverse problems, 19 (2003), 973-984.
doi: 10.1088/0266-5611/19/4/312. |
[2] |
G. Alessandrini, E. Sincich and S. Vessella, Stable determination of surface impedance on a rough obstacle by far field data, Inverse Problems and Imaging, 7 (2013), 341-351.
doi: 10.3934/ipi.2013.7.341. |
[3] |
M. Bellassoued, M. Choulli and A. Jbalia, Stability of the determination of the surface impedance of an obstacle from the scattering amplitude, Math. Methods Appl. Sci., 36 (2013), 2429-2448.
doi: 10.1002/mma.2762. |
[4] |
M. Bellassoued, J. Cheng and M. Choulli, Stability estimate for an inverse boundary coefficient problem in thermal imaging, J. Math Anal. Appl., 343 (2008), 328-336.
doi: 10.1016/j.jmaa.2008.01.066. |
[5] |
L. Bourgeois, About stability and regularization of ill-posed elliptic Cauchy problems: the case of $C^{1,1}$ domains, Math. Model. Numer. Anal., 44 (2010), 715-735.
doi: 10.1051/m2an/2010016. |
[6] |
S. Chaabane, I. Fellah, M. Jaoua and J. Leblond, Logarithmic stability estimates for a Robin coefficient in two-dimensional Laplace inverse problems, Inverse Problems, 20 (2004), 47-59.
doi: 10.1088/0266-5611/20/1/003. |
[7] |
S. Chaabane and M. Jaoua, Identification of Robin coefficients by the means of boundary measurements, Inverse Problems, 15 (1999), 1425-1438.
doi: 10.1088/0266-5611/15/6/303. |
[8] |
J. Cheng, M. Choulli and J. Lin, Stable determination of a boundary coefficient in an elliptic equation, Math. Models Methods Appl. Sci., 18 (2008), 107-123.
doi: 10.1142/S0218202508002620. |
[9] |
J. Cheng, M. Choulli and X. Yang, An iterative BEM for the inverse problem of detecting corrosion in a pipe, Numer. Math. J. Chinese Univ., 14 (2005), 252-266. |
[10] |
M. Choulli, Stability estimates for an inverse elliptic problem, J. Inverse Ill-Posed Probl., 10 (2002), 601-610.
doi: 10.1515/jiip.2002.10.6.601. |
[11] |
M. Choulli, An inverse problem in corrosion detection: Stability estimates, J. Inverse Ill-Posed Probl., 12 (2004), 349-367.
doi: 10.1515/1569394042248247. |
[12] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques, SMAI-Springer, Berlin, 2009.
doi: 10.1007/978-3-642-02460-3. |
[13] |
M. Choulli and F. Triki, New stability estimates for the inverse medium problem with internal data, SIAM J. Math. Anal., 47 (2015), 1778-1799.
doi: 10.1137/140988577. |
[14] |
M. Choulli, Applications of elliptic Carleman inequalities,, to appear in BCAM SpringerBriefs., ().
|
[15] |
D. Fasino and G. Inglese, An inverse Robin problem for Laplace's equation: Theoretical and numerical methods}, Inverse Problems, 15 (1999), 41-48.
doi: 10.1088/0266-5611/15/1/008. |
[16] |
G. Inglese, An inverse problem in corrosion detection, Inverse Problems, 13 (1997), 977-994.
doi: 10.1088/0266-5611/13/4/006. |
[17] |
E. Sincich, Stable determination of the surface impedance of an obstacle by far field measurements, SIAM J. Math. Anal., 38 (2006), 434-451.
doi: 10.1137/050631513. |
[18] |
E. Sincich, Lipschitz stability for the inverse Robin problem, Inverse Problems, 23 (2007), 1311-1326.
doi: 10.1088/0266-5611/23/3/027. |
[19] |
E. Sincich, Smoothness dependent stability in corrosion detection, J. Math. Anal. Appl., 426 (2015), 364-379.
doi: 10.1016/j.jmaa.2014.10.036. |
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