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The Factorization Method for an inverse fluid-solid interaction scattering problem
1. | Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany |
2. | Universidad Autonoma de Madrid, Departamento de Matemáticas, Madrid, Spain |
References:
[1] |
G. Alessandrini and L. Rondi, Determining a sound-soft polyhedral obstacle by a single far-field measurement, Proc. Am. Math. Soc., 6 (2005), 1685-1691.
doi: 10.1090/S0002-9939-05-07810-X. |
[2] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory: An Introduction," Interaction of Mechanics and Mathematics, Springer-Verlag, Berlin, 2006. |
[3] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[4] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium, Applicable Analysis, 88 (2009), 475-493.
doi: 10.1080/00036810802713966. |
[5] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," 2nd edition, Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1998. |
[6] |
D. Colton, L. Päivärinta and J. Sylvester, The interior transmission problem, Inverse Problems and Imaging, 1 (2007), 13-28.
doi: 10.3934/ipi.2007.1.13. |
[7] |
G. C. Hsiao, R. E. Kleinman and G. F. Roach, Weak solutions of fluid-solid interaction problems, Math. Nachr., 218 (2000), 139-163.
doi: 10.1002/1522-2616(200010)218:1<139::AID-MANA139>3.0.CO;2-S. |
[8] |
A. Kirsch, On the existence of transmission eigenvalues, Inverse Problems and Imaging, 3 (2009), 155-172.
doi: 10.3934/ipi.2009.3.155. |
[9] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford Lecture Series in Mathematics and its Applications, 36, Oxford University Press, Oxford, 2008. |
[10] |
H. Liu and J. Zou, Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers, Inverse Problems, 22 (2006), 515-524.
doi: 10.1088/0266-5611/22/2/008. |
[11] |
C. J. Luke and P. A. Martin, Fluid-solid interaction: Acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55 (1995), 904-922.
doi: 10.1137/S0036139993259027. |
[12] | |
[13] |
P. Monk and V. Selgas, An inverse fluid-solid interaction problem, Inverse Problems and Imaging, 3 (2009), 173-198.
doi: 10.3934/ipi.2009.3.173. |
[14] |
P. Monk and V. Selgas, Near field sampling type methods for the inverse fluid-solid interaction problem, Inverse Problems and Imaging, 5 (2011), 465-483.
doi: 10.3934/ipi.2011.5.465. |
[15] |
D. Natroshvili, S. Kharibegashvili and Z. Tediasvili, Direct and inverse fluid-structure interaction problems, Rendiconti di Matematica, Serie VII, 20 (2000), 57-92. |
[16] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753. |
show all references
References:
[1] |
G. Alessandrini and L. Rondi, Determining a sound-soft polyhedral obstacle by a single far-field measurement, Proc. Am. Math. Soc., 6 (2005), 1685-1691.
doi: 10.1090/S0002-9939-05-07810-X. |
[2] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory: An Introduction," Interaction of Mechanics and Mathematics, Springer-Verlag, Berlin, 2006. |
[3] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[4] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium, Applicable Analysis, 88 (2009), 475-493.
doi: 10.1080/00036810802713966. |
[5] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," 2nd edition, Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1998. |
[6] |
D. Colton, L. Päivärinta and J. Sylvester, The interior transmission problem, Inverse Problems and Imaging, 1 (2007), 13-28.
doi: 10.3934/ipi.2007.1.13. |
[7] |
G. C. Hsiao, R. E. Kleinman and G. F. Roach, Weak solutions of fluid-solid interaction problems, Math. Nachr., 218 (2000), 139-163.
doi: 10.1002/1522-2616(200010)218:1<139::AID-MANA139>3.0.CO;2-S. |
[8] |
A. Kirsch, On the existence of transmission eigenvalues, Inverse Problems and Imaging, 3 (2009), 155-172.
doi: 10.3934/ipi.2009.3.155. |
[9] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford Lecture Series in Mathematics and its Applications, 36, Oxford University Press, Oxford, 2008. |
[10] |
H. Liu and J. Zou, Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers, Inverse Problems, 22 (2006), 515-524.
doi: 10.1088/0266-5611/22/2/008. |
[11] |
C. J. Luke and P. A. Martin, Fluid-solid interaction: Acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55 (1995), 904-922.
doi: 10.1137/S0036139993259027. |
[12] | |
[13] |
P. Monk and V. Selgas, An inverse fluid-solid interaction problem, Inverse Problems and Imaging, 3 (2009), 173-198.
doi: 10.3934/ipi.2009.3.173. |
[14] |
P. Monk and V. Selgas, Near field sampling type methods for the inverse fluid-solid interaction problem, Inverse Problems and Imaging, 5 (2011), 465-483.
doi: 10.3934/ipi.2011.5.465. |
[15] |
D. Natroshvili, S. Kharibegashvili and Z. Tediasvili, Direct and inverse fluid-structure interaction problems, Rendiconti di Matematica, Serie VII, 20 (2000), 57-92. |
[16] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753. |
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