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Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary
| 1. | Institut de Mathématiques de Marseille, CNRS, UMR 7373, École Centrale, Aix-Marseille Université, 13453 Marseille, France |
| 2. | Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui Province, 230026, China |
| 3. | Aix-Marseille Université de Toulon, CNRS, CPT, 13288 Marseille, France |
References:
| [1] |
M. Bellassoued, Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation, Inverse Problems, 20 (2004), 1033-1052.
doi: 10.1088/0266-5611/20/4/003. |
| [2] |
M. Bellassoued, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients, Applicable Analysis, 83 (2004), 983-1014.
doi: 10.1080/0003681042000221678. |
| [3] |
M. Bellassoued, M. Cristofol and E. Soccorsi, Inverse boundary value problem for the dynamical heterogeneous Maxwell's system, Inverse Problems, 28 (2012), 095009, 18pp.
doi: 10.1088/0266-5611/28/9/095009. |
| [4] |
M. Bellassoued, M. Choulli and M. Yamamoto, Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem, J. Diff. Equat., 247 (2009), 465-494.
doi: 10.1016/j.jde.2009.03.024. |
| [5] |
M. Bellassoued, D. Jellali and M. Yamamoto, Lipschitz stability in in an inverse problem for a hyperbolic equation with a finite set of boundary data, Applicable Analysis, 87 (2008), 1105-1119.
doi: 10.1080/00036810802369231. |
| [6] |
M. Bellassoued and M. Yamamoto, Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation, J. Math. Pures Appl., 85 (2006), 193-224.
doi: 10.1016/j.matpur.2005.02.004. |
| [7] |
M. Bellassoued and M. Yamamoto, Determination of a coefficient in the wave equation with a single measurement, Applicable Analysis, 87 (2008), 901-920.
doi: 10.1080/00036810802369249. |
| [8] |
A. L. Bukhgeim and M. V. Klibanov, Global uniqueness of class of multidimentional inverse problems, Soviet Math. Dokl., 24 (1981), 244-247. |
| [9] |
L. Cardoulis, M. Cristofol and P. Gaitan, Inverse problem for the Schrödinger operator in an unbounded strip, C. R. Math. Acad. Sci. Paris, 346 (2008), 635-640.
doi: 10.1016/j.crma.2008.04.004. |
| [10] |
L. C. Evans, Partial Differential Equations, Amer. Math. Soc., Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.
doi: 10.1090/gsm/019. |
| [11] |
O. Imanuvilov and M. Yamamoto, Global Lipschitz stability in an inverse hyperbolic problem by interior observations, Inverse Problems, 17 (2001), 717-728.
doi: 10.1088/0266-5611/17/4/310. |
| [12] |
O. Imanuvilov and M. Yamamoto, Determination of a coefficient in an acoustic equation with single measurement, Inverse Problems, 19 (2003), 157-171.
doi: 10.1088/0266-5611/19/1/309. |
| [13] |
V. Isakov and Z. Sun, Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8 (1992), 193-206.
doi: 10.1088/0266-5611/8/2/003. |
| [14] |
V. Isakov, Inverse Problems for Partial Differential Equations, Springer-Verlag, Berlin, 2006. |
| [15] |
Y. Kian, Q. S. Phan and E. Soccorsi, Carleman estimate for infinite cylindrical quantum domains and application to inverse problems, Inverse Problems, 30 (2014), 055016, 16pp.
doi: 10.1088/0266-5611/30/5/055016. |
| [16] |
Y. Kian, Q. S. Phan and E. Soccorsi, Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains, Journal of Mathematical Analysis and Applications, 426 (2015), 194-210.
doi: 10.1016/j.jmaa.2015.01.028. |
| [17] |
M. V. Klibanov and J. Malinsky, Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data, Inverse Problems, 7 (1991), 577-596.
doi: 10.1088/0266-5611/7/4/007. |
| [18] |
M. V. Klibanov and M. Yamamoto, Lipschitz stability of an inverse problem for an accoustic equation, Applicable Analysis, 85 (2006), 515-538.
doi: 10.1080/00036810500474788. |
| [19] |
J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, vol. 1, Dunod, 1968. |
| [20] |
P. Stefanov and G. Uhlmann, Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media, J. Funct. Anal., 154 (1998), 330-358.
doi: 10.1006/jfan.1997.3188. |
| [21] |
M. Yamamoto, Uniqueness and stability in multidimensional hyperbolic inverse problems, J. Math. Pures Appl., 78 (1999), 65-98.
doi: 10.1016/S0021-7824(99)80010-5. |
show all references
References:
| [1] |
M. Bellassoued, Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation, Inverse Problems, 20 (2004), 1033-1052.
doi: 10.1088/0266-5611/20/4/003. |
| [2] |
M. Bellassoued, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients, Applicable Analysis, 83 (2004), 983-1014.
doi: 10.1080/0003681042000221678. |
| [3] |
M. Bellassoued, M. Cristofol and E. Soccorsi, Inverse boundary value problem for the dynamical heterogeneous Maxwell's system, Inverse Problems, 28 (2012), 095009, 18pp.
doi: 10.1088/0266-5611/28/9/095009. |
| [4] |
M. Bellassoued, M. Choulli and M. Yamamoto, Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem, J. Diff. Equat., 247 (2009), 465-494.
doi: 10.1016/j.jde.2009.03.024. |
| [5] |
M. Bellassoued, D. Jellali and M. Yamamoto, Lipschitz stability in in an inverse problem for a hyperbolic equation with a finite set of boundary data, Applicable Analysis, 87 (2008), 1105-1119.
doi: 10.1080/00036810802369231. |
| [6] |
M. Bellassoued and M. Yamamoto, Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation, J. Math. Pures Appl., 85 (2006), 193-224.
doi: 10.1016/j.matpur.2005.02.004. |
| [7] |
M. Bellassoued and M. Yamamoto, Determination of a coefficient in the wave equation with a single measurement, Applicable Analysis, 87 (2008), 901-920.
doi: 10.1080/00036810802369249. |
| [8] |
A. L. Bukhgeim and M. V. Klibanov, Global uniqueness of class of multidimentional inverse problems, Soviet Math. Dokl., 24 (1981), 244-247. |
| [9] |
L. Cardoulis, M. Cristofol and P. Gaitan, Inverse problem for the Schrödinger operator in an unbounded strip, C. R. Math. Acad. Sci. Paris, 346 (2008), 635-640.
doi: 10.1016/j.crma.2008.04.004. |
| [10] |
L. C. Evans, Partial Differential Equations, Amer. Math. Soc., Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.
doi: 10.1090/gsm/019. |
| [11] |
O. Imanuvilov and M. Yamamoto, Global Lipschitz stability in an inverse hyperbolic problem by interior observations, Inverse Problems, 17 (2001), 717-728.
doi: 10.1088/0266-5611/17/4/310. |
| [12] |
O. Imanuvilov and M. Yamamoto, Determination of a coefficient in an acoustic equation with single measurement, Inverse Problems, 19 (2003), 157-171.
doi: 10.1088/0266-5611/19/1/309. |
| [13] |
V. Isakov and Z. Sun, Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8 (1992), 193-206.
doi: 10.1088/0266-5611/8/2/003. |
| [14] |
V. Isakov, Inverse Problems for Partial Differential Equations, Springer-Verlag, Berlin, 2006. |
| [15] |
Y. Kian, Q. S. Phan and E. Soccorsi, Carleman estimate for infinite cylindrical quantum domains and application to inverse problems, Inverse Problems, 30 (2014), 055016, 16pp.
doi: 10.1088/0266-5611/30/5/055016. |
| [16] |
Y. Kian, Q. S. Phan and E. Soccorsi, Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains, Journal of Mathematical Analysis and Applications, 426 (2015), 194-210.
doi: 10.1016/j.jmaa.2015.01.028. |
| [17] |
M. V. Klibanov and J. Malinsky, Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data, Inverse Problems, 7 (1991), 577-596.
doi: 10.1088/0266-5611/7/4/007. |
| [18] |
M. V. Klibanov and M. Yamamoto, Lipschitz stability of an inverse problem for an accoustic equation, Applicable Analysis, 85 (2006), 515-538.
doi: 10.1080/00036810500474788. |
| [19] |
J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, vol. 1, Dunod, 1968. |
| [20] |
P. Stefanov and G. Uhlmann, Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media, J. Funct. Anal., 154 (1998), 330-358.
doi: 10.1006/jfan.1997.3188. |
| [21] |
M. Yamamoto, Uniqueness and stability in multidimensional hyperbolic inverse problems, J. Math. Pures Appl., 78 (1999), 65-98.
doi: 10.1016/S0021-7824(99)80010-5. |
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