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Reconstruction of penetrable obstacles in the anisotropic acoustic scattering
1. | Department of Mathematics, National Taiwan University, Taipei 106, Taiwan |
References:
[1] |
L, Hörmander, The Analysis of Linear Partial Differential Operators III: Pseudo-differential Operators, volume 274. Springer Science & Business Media, 2007. |
[2] |
M. Ikehata, How to draw a picture of an unknown inclusion from boundary measurements, Two mathematical inversion algorithms, J. Inverse Ill-Posed Probl., 7 (1999), 255-271.
doi: 10.1515/jiip.1999.7.3.255. |
[3] |
M. Ikehata, Enclosing a polygonal cavity in a two-dimensional bounded domain from cauchy data, Inverse Problems, 15 (1999), 1231-1241.
doi: 10.1088/0266-5611/15/5/308. |
[4] |
M. Ikehata, The enclosure method and its applications, In Analytic extension formulas and their applications, pages 87-103. Springer, 2001.
doi: 10.1007/978-1-4757-3298-6_7. |
[5] |
P. D. Lax, A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations, Communications on Pure and Applied Mathematics, 9 (1956), 747-766.
doi: 10.1002/cpa.3160090407. |
[6] |
B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, In Annales de l'institut Fourier, volume 6, pages 271-355. Institut Fourier, 1956. |
[7] |
V. G. Maz'ja, Sobolev Spaces, Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1985.
doi: 10.1007/978-3-662-09922-3. |
[8] |
N. G. Meyers, Lp estimate for the gradient of solutions of second order elliptic divergence equations, Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze, 17 (1963), 189-206. |
[9] |
S. Nagayasu, G. Uhlmann and J.-N. Wang, Reconstruction of penetrable obstacles in acoustic scattering, SIAM Journal on Mathematical Analysis, 43 (2011), 189-211.
doi: 10.1137/09076218X. |
[10] |
G. Nakamura, Applications of the oscillating-decaying solutions to inverse problems, In New analytic and geometric methods in inverse problems, pages 353-365. Springer, 2004. |
[11] |
G. Nakamura, G. Uhlmann and J.-N. Wang, Oscillating-decaying solutions, runge approximation property for the anisotropic elasticity system and their applications to inverse problems, Journal de mathématiques pures et appliquées, 84 (2005), 21-54.
doi: 10.1016/j.matpur.2004.09.002. |
[12] |
M. Sini and K. Yoshida, On the reconstruction of interfaces using complex geometrical optics solutions for the acoustic case, Inverse Problems, 28 (2012), 055013.
doi: 10.1088/0266-5611/28/5/055013. |
[13] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Annals of Mathematics, 125 (1987), 153-169.
doi: 10.2307/1971291. |
[14] |
H. Takuwa, G. Uhlmann and J.-N. Wang, Complex geometrical optics solutions for anisotropic equations and applications, Journal of Inverse and Ill-posed Problems, 16 (2008), 791-804.
doi: 10.1515/JIIP.2008.049. |
[15] |
G. Uhlmann and J.-N. Wang, Reconstructing discontinuities using complex geometrical optics solutions, SIAM Journal on Applied Mathematics, 68 (2008), 1026-1044.
doi: 10.1137/060676350. |
show all references
References:
[1] |
L, Hörmander, The Analysis of Linear Partial Differential Operators III: Pseudo-differential Operators, volume 274. Springer Science & Business Media, 2007. |
[2] |
M. Ikehata, How to draw a picture of an unknown inclusion from boundary measurements, Two mathematical inversion algorithms, J. Inverse Ill-Posed Probl., 7 (1999), 255-271.
doi: 10.1515/jiip.1999.7.3.255. |
[3] |
M. Ikehata, Enclosing a polygonal cavity in a two-dimensional bounded domain from cauchy data, Inverse Problems, 15 (1999), 1231-1241.
doi: 10.1088/0266-5611/15/5/308. |
[4] |
M. Ikehata, The enclosure method and its applications, In Analytic extension formulas and their applications, pages 87-103. Springer, 2001.
doi: 10.1007/978-1-4757-3298-6_7. |
[5] |
P. D. Lax, A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations, Communications on Pure and Applied Mathematics, 9 (1956), 747-766.
doi: 10.1002/cpa.3160090407. |
[6] |
B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, In Annales de l'institut Fourier, volume 6, pages 271-355. Institut Fourier, 1956. |
[7] |
V. G. Maz'ja, Sobolev Spaces, Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1985.
doi: 10.1007/978-3-662-09922-3. |
[8] |
N. G. Meyers, Lp estimate for the gradient of solutions of second order elliptic divergence equations, Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze, 17 (1963), 189-206. |
[9] |
S. Nagayasu, G. Uhlmann and J.-N. Wang, Reconstruction of penetrable obstacles in acoustic scattering, SIAM Journal on Mathematical Analysis, 43 (2011), 189-211.
doi: 10.1137/09076218X. |
[10] |
G. Nakamura, Applications of the oscillating-decaying solutions to inverse problems, In New analytic and geometric methods in inverse problems, pages 353-365. Springer, 2004. |
[11] |
G. Nakamura, G. Uhlmann and J.-N. Wang, Oscillating-decaying solutions, runge approximation property for the anisotropic elasticity system and their applications to inverse problems, Journal de mathématiques pures et appliquées, 84 (2005), 21-54.
doi: 10.1016/j.matpur.2004.09.002. |
[12] |
M. Sini and K. Yoshida, On the reconstruction of interfaces using complex geometrical optics solutions for the acoustic case, Inverse Problems, 28 (2012), 055013.
doi: 10.1088/0266-5611/28/5/055013. |
[13] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Annals of Mathematics, 125 (1987), 153-169.
doi: 10.2307/1971291. |
[14] |
H. Takuwa, G. Uhlmann and J.-N. Wang, Complex geometrical optics solutions for anisotropic equations and applications, Journal of Inverse and Ill-posed Problems, 16 (2008), 791-804.
doi: 10.1515/JIIP.2008.049. |
[15] |
G. Uhlmann and J.-N. Wang, Reconstructing discontinuities using complex geometrical optics solutions, SIAM Journal on Applied Mathematics, 68 (2008), 1026-1044.
doi: 10.1137/060676350. |
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