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On recovery of an inhomogeneous cavity in inverse acoustic scattering
1. | School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, China |
2. | School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China |
Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [
References:
[1] |
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. |
[2] |
F. Cakoni and D. Colton, Qualitative Method in Inverse Scattering Theory, Springer. Berlin, 2006. |
[3] |
F. Cakoni, D. Colton and S. Meng,
The inverse scattering problem for a penetrable cavity with internal measurements, AMS Contemp. Math., 615 (2014), 71-88.
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[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. |
[5] |
P. Jakubik and R. Potthast,
Testing the integrity of some cavity-the Cauchy problem and the range test, Appl. Numer. Math., 58 (2008), 899-914.
doi: 10.1016/j.apnum.2007.04.007. |
[6] |
X. Liu, The factorization method for cavities, Inverse Problems, 30 (2014), 015006, 18pp. |
[7] |
S. Meng, H. Haddar and F. Cakoni, The factorization method for a cavity in an inhomogeneous medium, Inverse Problems, 30 (2014), 045008, 20pp. |
[8] |
H. Qin and F. Cakoni, Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem, Inverse Problems, 27 (2011), 035005, 17pp. |
[9] |
H. Qin and D. Colton,
The inverse scattering problem for cavities, J. Appl. Numer. Math., 62 (2015), 699-708.
doi: 10.1016/j.apnum.2010.10.011. |
[10] |
J. Yang, H. Zhang and B. Zhang, Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles, arXiv: 1305.0917. Google Scholar |
[11] |
F. Zeng, F. Cakoni and J. Sun, An inverse electromagnetic scattering problem for a cavity, Inverse Problems, 27 (2011), 125002, 17pp. |
show all references
References:
[1] |
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. |
[2] |
F. Cakoni and D. Colton, Qualitative Method in Inverse Scattering Theory, Springer. Berlin, 2006. |
[3] |
F. Cakoni, D. Colton and S. Meng,
The inverse scattering problem for a penetrable cavity with internal measurements, AMS Contemp. Math., 615 (2014), 71-88.
|
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. |
[5] |
P. Jakubik and R. Potthast,
Testing the integrity of some cavity-the Cauchy problem and the range test, Appl. Numer. Math., 58 (2008), 899-914.
doi: 10.1016/j.apnum.2007.04.007. |
[6] |
X. Liu, The factorization method for cavities, Inverse Problems, 30 (2014), 015006, 18pp. |
[7] |
S. Meng, H. Haddar and F. Cakoni, The factorization method for a cavity in an inhomogeneous medium, Inverse Problems, 30 (2014), 045008, 20pp. |
[8] |
H. Qin and F. Cakoni, Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem, Inverse Problems, 27 (2011), 035005, 17pp. |
[9] |
H. Qin and D. Colton,
The inverse scattering problem for cavities, J. Appl. Numer. Math., 62 (2015), 699-708.
doi: 10.1016/j.apnum.2010.10.011. |
[10] |
J. Yang, H. Zhang and B. Zhang, Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles, arXiv: 1305.0917. Google Scholar |
[11] |
F. Zeng, F. Cakoni and J. Sun, An inverse electromagnetic scattering problem for a cavity, Inverse Problems, 27 (2011), 125002, 17pp. |


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