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On the inverse doping profile problem
The Green function of the interior transmission problem and its applications
1. | Department of Mathematics of Inha University, Incheon 402-751, South Korea |
2. | Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
3. | Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz A-4040, Australia |
References:
[1] |
M. F. Ben Hassen, O. Ivanyshyn and M. Sini, Three-dimensional acoustic scattering by complex obstacles. The accuracy issue,, Inverse Problems, 26 (2010).
|
[2] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory. An Introduction,'', Interaction of Mechanics and Mathematics, (2006).
|
[3] |
F. Cakoni, D. Colton and H. Haddar, The linear sampling method for anisotropic media,, J. Comput. Appl. Math., 146 (2002), 285.
doi: 10.1016/S0377-0427(02)00361-8. |
[4] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium,, Appl. Anal., 88 (2009), 475.
doi: 10.1080/00036810802713966. |
[5] |
F. Cakoni, G. Nakamura, M. Sini and N. Zeev, The identification of a partially coated dielectric from far field measurements,, Applicable Analysis, 89 (2010), 67.
doi: 10.1080/00036810903437820. |
[6] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region,, Inverse Problems, 12 (1996), 383.
doi: 10.1088/0266-5611/12/4/003. |
[7] |
D. Colton, L. Paivarinta and J. Sylvester, The interior transmission problem,, Inverse Problems and Imaging, 1 (2007), 13.
|
[8] |
J. Chazarain and A. Piriou, "Introduction to the Theory of Linear Partial Differential Equations,'', North-Holland, (1982).
|
[9] |
M. Hitrik, K. Krupchyk, P. Ola and L. Paivarinta, The interior transmission problem and bounds on transmission eigenvalues,, Math. Res. Lett., 18 (2011), 279.
|
[10] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems,'', Oxford Lecture Series in Mathematics and its Applications, (2008).
|
[11] |
H. Kumanogo, "Pseudodifferential Operators,'', MIT Press, (1981).
|
[12] |
E. Lakshtanov and B. Vainberg, Ellipticity in the interior transmission problem in anisotropic media,, SIAM J. Math. Anal., 44 (2012), 1165.
|
[13] |
J. J. Liu, G. Nakamura and M. Sini, Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder,, SIAM J. Appl. Math., 67 (2007), 1124.
doi: 10.1137/060654220. |
[14] |
J. Liu and M. Sini, On the accuracy of the numerical detection of complex obstacles from far field data using the probe method,, SIAM J. Scient. Comp., 31 (2009), 2665.
doi: 10.1137/080718024. |
[15] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,'', Cambridge University Press, (2000).
|
[16] |
G. Nakamura and M. Sini, Obstacle and boundary determination from scattering data,, SIAM J. Math. Anal., 39 (2007), 819.
doi: 10.1137/060658667. |
[17] |
L. Paivarinta and J. Sylvester, Transmission eigenvalues,, SIAM J. Math. Anal., 40 (2008), 738.
doi: 10.1137/070697525. |
[18] |
R. Seeley, The resolvent of an elliptic boundary problem,, Amer. J. of Math., 91 (1969), 889.
doi: 10.2307/2373309. |
[19] |
N. Shimakura, "Partial Differential Operators of Elliptic Type,'', AMS, (1992).
|
[20] |
M. E. Taylor, "Partial Differential Equations II. Qualitative Studies of Linear Equations,'', Applied Mathematical Sciences, (1996).
|
[21] |
N. T. Thanh and M. Sini, An analysis of the accuracy of the linear sampling method for an acoustic inverse obstacle scattering problem,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/1/015010. |
[22] |
N. T. Thanh and M. Sini, Accuracy of the linear sampling method for inverse obstacle scattering: effect of geometrical and physical parameters,, Inverse Problems, 26 (2010).
|
[23] |
F. Treves, "Introduction to Pseudodifferential and Fourier Integral Operators,'', 1, 1 (1980).
|
[24] |
N. Valdivia, Uniqueness in inverse obstacle scattering with conductive boundary conditions,, Appl. Anal., 83 (2004), 825.
doi: 10.1080/00036810410001689283. |
show all references
References:
[1] |
M. F. Ben Hassen, O. Ivanyshyn and M. Sini, Three-dimensional acoustic scattering by complex obstacles. The accuracy issue,, Inverse Problems, 26 (2010).
|
[2] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory. An Introduction,'', Interaction of Mechanics and Mathematics, (2006).
|
[3] |
F. Cakoni, D. Colton and H. Haddar, The linear sampling method for anisotropic media,, J. Comput. Appl. Math., 146 (2002), 285.
doi: 10.1016/S0377-0427(02)00361-8. |
[4] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium,, Appl. Anal., 88 (2009), 475.
doi: 10.1080/00036810802713966. |
[5] |
F. Cakoni, G. Nakamura, M. Sini and N. Zeev, The identification of a partially coated dielectric from far field measurements,, Applicable Analysis, 89 (2010), 67.
doi: 10.1080/00036810903437820. |
[6] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region,, Inverse Problems, 12 (1996), 383.
doi: 10.1088/0266-5611/12/4/003. |
[7] |
D. Colton, L. Paivarinta and J. Sylvester, The interior transmission problem,, Inverse Problems and Imaging, 1 (2007), 13.
|
[8] |
J. Chazarain and A. Piriou, "Introduction to the Theory of Linear Partial Differential Equations,'', North-Holland, (1982).
|
[9] |
M. Hitrik, K. Krupchyk, P. Ola and L. Paivarinta, The interior transmission problem and bounds on transmission eigenvalues,, Math. Res. Lett., 18 (2011), 279.
|
[10] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems,'', Oxford Lecture Series in Mathematics and its Applications, (2008).
|
[11] |
H. Kumanogo, "Pseudodifferential Operators,'', MIT Press, (1981).
|
[12] |
E. Lakshtanov and B. Vainberg, Ellipticity in the interior transmission problem in anisotropic media,, SIAM J. Math. Anal., 44 (2012), 1165.
|
[13] |
J. J. Liu, G. Nakamura and M. Sini, Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder,, SIAM J. Appl. Math., 67 (2007), 1124.
doi: 10.1137/060654220. |
[14] |
J. Liu and M. Sini, On the accuracy of the numerical detection of complex obstacles from far field data using the probe method,, SIAM J. Scient. Comp., 31 (2009), 2665.
doi: 10.1137/080718024. |
[15] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,'', Cambridge University Press, (2000).
|
[16] |
G. Nakamura and M. Sini, Obstacle and boundary determination from scattering data,, SIAM J. Math. Anal., 39 (2007), 819.
doi: 10.1137/060658667. |
[17] |
L. Paivarinta and J. Sylvester, Transmission eigenvalues,, SIAM J. Math. Anal., 40 (2008), 738.
doi: 10.1137/070697525. |
[18] |
R. Seeley, The resolvent of an elliptic boundary problem,, Amer. J. of Math., 91 (1969), 889.
doi: 10.2307/2373309. |
[19] |
N. Shimakura, "Partial Differential Operators of Elliptic Type,'', AMS, (1992).
|
[20] |
M. E. Taylor, "Partial Differential Equations II. Qualitative Studies of Linear Equations,'', Applied Mathematical Sciences, (1996).
|
[21] |
N. T. Thanh and M. Sini, An analysis of the accuracy of the linear sampling method for an acoustic inverse obstacle scattering problem,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/1/015010. |
[22] |
N. T. Thanh and M. Sini, Accuracy of the linear sampling method for inverse obstacle scattering: effect of geometrical and physical parameters,, Inverse Problems, 26 (2010).
|
[23] |
F. Treves, "Introduction to Pseudodifferential and Fourier Integral Operators,'', 1, 1 (1980).
|
[24] |
N. Valdivia, Uniqueness in inverse obstacle scattering with conductive boundary conditions,, Appl. Anal., 83 (2004), 825.
doi: 10.1080/00036810410001689283. |
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