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Stability of the determination of a coefficient for wave equations in an infinite waveguide
1. | CPT, UMR CNRS 7332, Aix Marseille Université, Campus de Luminy, Case 907, 13288 Marseille, cedex 9, France |
References:
[1] |
M. Bellassoued, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients,, Appl. Anal., 83 (2004), 983.
doi: 10.1080/0003681042000221678. |
[2] |
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.
doi: 10.1016/j.jde.2009.03.024. |
[3] |
M. Bellassoued, D. Jellali and M. Yamamoto, Lipschitz stability for a hyperbolic inverse problem by finite local boundary data,, Appl. Anal., 85 (2006), 1219.
doi: 10.1080/00036810600787873. |
[4] |
M. Bellassoued, D. Jellali and M. Yamamoto, Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map,, J. Math. Anal. Appl, 343 (2008), 1036.
doi: 10.1016/j.jmaa.2008.01.098. |
[5] |
A. L. Bukhgeim and M. V. Klibanov, Global uniqueness of class of multidimensional inverse problems,, Sov. Math. Dokl., 24 (1981), 244. Google Scholar |
[6] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques,, Mathématiques et Applications, (2009). Google Scholar |
[7] |
M. Choulli and E. Soccorsi, Some inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain,, preprint, (). Google Scholar |
[8] |
G. Eskin, A new approach to hyperbolic inverse problems,, Inverse Problems, 22 (2006), 815.
doi: 10.1088/0266-5611/22/3/005. |
[9] |
G. Eskin, Inverse hyperbolic problems with time-dependent coefficients,, Comm. PDE, 32 (2007), 1737.
doi: 10.1080/03605300701382340. |
[10] |
G. Eskin, Inverse problems for the Schrödinger equations with time-dependent electromagnetic potentials and the Aharonov-Bohm effect,, J. Math. Phys., 49 (2008), 1.
doi: 10.1063/1.2841329. |
[11] |
C. Hamaker, K. T. Smith, D. C. Solomonand and S. C. Wagner, The divergent beam x-ray transform,, Rocky Mountain J. Math., 10 (1980), 253.
doi: 10.1216/RMJ-1980-10-1-253. |
[12] |
M. Ikehata, Inverse conductivity problem in the infinite slab,, Inverse Problems, 17 (2001), 437.
doi: 10.1088/0266-5611/17/3/305. |
[13] |
O. Yu. Imanuvilov and M. Yamamoto, Global uniqueness and stability in determining coefficients of wave equations,, Comm. PDE, 26 (2001), 1409.
doi: 10.1081/PDE-100106139. |
[14] |
V. Isakov, An inverse hyperbolic problem with many boundary measurements,, Comm. PDE, 16 (1991), 1183.
doi: 10.1080/03605309108820794. |
[15] |
V. Isakov and Z. Sun, Stability estimates for hyperbolic inverse problems with local boundary data,, Inverse Problems, 8 (1992), 193.
doi: 10.1088/0266-5611/8/2/003. |
[16] |
M. V. Klibanov, Inverse problems and Carleman estimates,, Inverse Problems, 8 (1992), 575.
doi: 10.1088/0266-5611/8/4/009. |
[17] |
K. Krupchyk , M. Lassas and G. Uhlmann, Inverse Problems With Partial Data for a Magnetic Schrödinger Operator in an Infinite Slab and on a Bounded Domain,, Communications in Mathematical Physics, 312 (2012), 87.
doi: 10.1007/s00220-012-1431-1. |
[18] |
I. Lasiecka, J.-L. Lions and R. Triggiani, Non homogeneous boundary value problems for second order hyperbolic operators,, J. Math. Pures Appl., 65 (1986), 149.
|
[19] |
X. Li and G. Uhlmann, Inverse problems with partial data in a slab,, Inverse Probl. Imaging, 4 (2010), 449.
doi: 10.3934/ipi.2010.4.449. |
[20] |
J-L. Lions and E. Magenes, Problèmes Aux Limites Non Homogènes et Applications,, Vol. I, (1968). Google Scholar |
[21] |
J-L. Lions and E. Magenes, Problèmes Aux Limites Non Homogènes et Applications,, Vol. II, (1968). Google Scholar |
[22] |
S-I. Nakamura, Uniqueness for an Inverse Problem for the Wave Equation in the Half Space,, Tokyo J. of Math., 19 (1996), 187.
doi: 10.3836/tjm/1270043228. |
[23] |
F. Natterer, The Mathematics of Computarized Tomography,, John Wiley & Sons, (1986). Google Scholar |
[24] |
Rakesh, Reconstruction for an inverse problem for the wave equation with constant velocity,, Inverse Problems, 6 (1990), 91.
doi: 10.1088/0266-5611/6/1/009. |
[25] |
Rakesh, An inverse problem for the wave equation in the half plane,, Inverse Problems, 9 (1993), 433.
doi: 10.1088/0266-5611/9/3/005. |
[26] |
Rakesh and W. Symes, Uniqueness for an inverse problem for the wave equation,, Comm. PDE, 13 (1988), 87.
doi: 10.1080/03605308808820539. |
[27] |
A. Ramm and J. Sjöstrand, An inverse problem of the wave equation,, Math. Z., 206 (1991), 119.
doi: 10.1007/BF02571330. |
[28] |
M. Salo and J. N. Wang, Complex spherical waves and inverse problems in unbounded domains,, Inverse Problems, 22 (2006), 2299.
doi: 10.1088/0266-5611/22/6/023. |
[29] |
P. Stefanov and G. Uhlmann, Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media,, J. Funct. Anal., 154 (1998), 330.
doi: 10.1006/jfan.1997.3188. |
show all references
References:
[1] |
M. Bellassoued, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients,, Appl. Anal., 83 (2004), 983.
doi: 10.1080/0003681042000221678. |
[2] |
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.
doi: 10.1016/j.jde.2009.03.024. |
[3] |
M. Bellassoued, D. Jellali and M. Yamamoto, Lipschitz stability for a hyperbolic inverse problem by finite local boundary data,, Appl. Anal., 85 (2006), 1219.
doi: 10.1080/00036810600787873. |
[4] |
M. Bellassoued, D. Jellali and M. Yamamoto, Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map,, J. Math. Anal. Appl, 343 (2008), 1036.
doi: 10.1016/j.jmaa.2008.01.098. |
[5] |
A. L. Bukhgeim and M. V. Klibanov, Global uniqueness of class of multidimensional inverse problems,, Sov. Math. Dokl., 24 (1981), 244. Google Scholar |
[6] |
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques,, Mathématiques et Applications, (2009). Google Scholar |
[7] |
M. Choulli and E. Soccorsi, Some inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain,, preprint, (). Google Scholar |
[8] |
G. Eskin, A new approach to hyperbolic inverse problems,, Inverse Problems, 22 (2006), 815.
doi: 10.1088/0266-5611/22/3/005. |
[9] |
G. Eskin, Inverse hyperbolic problems with time-dependent coefficients,, Comm. PDE, 32 (2007), 1737.
doi: 10.1080/03605300701382340. |
[10] |
G. Eskin, Inverse problems for the Schrödinger equations with time-dependent electromagnetic potentials and the Aharonov-Bohm effect,, J. Math. Phys., 49 (2008), 1.
doi: 10.1063/1.2841329. |
[11] |
C. Hamaker, K. T. Smith, D. C. Solomonand and S. C. Wagner, The divergent beam x-ray transform,, Rocky Mountain J. Math., 10 (1980), 253.
doi: 10.1216/RMJ-1980-10-1-253. |
[12] |
M. Ikehata, Inverse conductivity problem in the infinite slab,, Inverse Problems, 17 (2001), 437.
doi: 10.1088/0266-5611/17/3/305. |
[13] |
O. Yu. Imanuvilov and M. Yamamoto, Global uniqueness and stability in determining coefficients of wave equations,, Comm. PDE, 26 (2001), 1409.
doi: 10.1081/PDE-100106139. |
[14] |
V. Isakov, An inverse hyperbolic problem with many boundary measurements,, Comm. PDE, 16 (1991), 1183.
doi: 10.1080/03605309108820794. |
[15] |
V. Isakov and Z. Sun, Stability estimates for hyperbolic inverse problems with local boundary data,, Inverse Problems, 8 (1992), 193.
doi: 10.1088/0266-5611/8/2/003. |
[16] |
M. V. Klibanov, Inverse problems and Carleman estimates,, Inverse Problems, 8 (1992), 575.
doi: 10.1088/0266-5611/8/4/009. |
[17] |
K. Krupchyk , M. Lassas and G. Uhlmann, Inverse Problems With Partial Data for a Magnetic Schrödinger Operator in an Infinite Slab and on a Bounded Domain,, Communications in Mathematical Physics, 312 (2012), 87.
doi: 10.1007/s00220-012-1431-1. |
[18] |
I. Lasiecka, J.-L. Lions and R. Triggiani, Non homogeneous boundary value problems for second order hyperbolic operators,, J. Math. Pures Appl., 65 (1986), 149.
|
[19] |
X. Li and G. Uhlmann, Inverse problems with partial data in a slab,, Inverse Probl. Imaging, 4 (2010), 449.
doi: 10.3934/ipi.2010.4.449. |
[20] |
J-L. Lions and E. Magenes, Problèmes Aux Limites Non Homogènes et Applications,, Vol. I, (1968). Google Scholar |
[21] |
J-L. Lions and E. Magenes, Problèmes Aux Limites Non Homogènes et Applications,, Vol. II, (1968). Google Scholar |
[22] |
S-I. Nakamura, Uniqueness for an Inverse Problem for the Wave Equation in the Half Space,, Tokyo J. of Math., 19 (1996), 187.
doi: 10.3836/tjm/1270043228. |
[23] |
F. Natterer, The Mathematics of Computarized Tomography,, John Wiley & Sons, (1986). Google Scholar |
[24] |
Rakesh, Reconstruction for an inverse problem for the wave equation with constant velocity,, Inverse Problems, 6 (1990), 91.
doi: 10.1088/0266-5611/6/1/009. |
[25] |
Rakesh, An inverse problem for the wave equation in the half plane,, Inverse Problems, 9 (1993), 433.
doi: 10.1088/0266-5611/9/3/005. |
[26] |
Rakesh and W. Symes, Uniqueness for an inverse problem for the wave equation,, Comm. PDE, 13 (1988), 87.
doi: 10.1080/03605308808820539. |
[27] |
A. Ramm and J. Sjöstrand, An inverse problem of the wave equation,, Math. Z., 206 (1991), 119.
doi: 10.1007/BF02571330. |
[28] |
M. Salo and J. N. Wang, Complex spherical waves and inverse problems in unbounded domains,, Inverse Problems, 22 (2006), 2299.
doi: 10.1088/0266-5611/22/6/023. |
[29] |
P. Stefanov and G. Uhlmann, Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media,, J. Funct. Anal., 154 (1998), 330.
doi: 10.1006/jfan.1997.3188. |
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