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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).
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[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.
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.
doi: 10.1088/0266-5611/15/5/308. |
[4] |
M. Ikehata, The enclosure method and its applications,, In Analytic extension formulas and their applications, (2001), 87.
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.
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, (1956), 271.
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[7] |
V. G. Maz'ja, Sobolev Spaces,, Springer Series in Soviet Mathematics. Springer-Verlag, (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.
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[9] |
S. Nagayasu, G. Uhlmann and J.-N. Wang, Reconstruction of penetrable obstacles in acoustic scattering,, SIAM Journal on Mathematical Analysis, 43 (2011), 189.
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, (2004), 353.
|
[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.
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).
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.
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.
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.
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.
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.
doi: 10.1088/0266-5611/15/5/308. |
[4] |
M. Ikehata, The enclosure method and its applications,, In Analytic extension formulas and their applications, (2001), 87.
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.
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, (1956), 271.
|
[7] |
V. G. Maz'ja, Sobolev Spaces,, Springer Series in Soviet Mathematics. Springer-Verlag, (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.
|
[9] |
S. Nagayasu, G. Uhlmann and J.-N. Wang, Reconstruction of penetrable obstacles in acoustic scattering,, SIAM Journal on Mathematical Analysis, 43 (2011), 189.
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, (2004), 353.
|
[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.
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).
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.
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.
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.
doi: 10.1137/060676350. |
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