Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core
This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the soluti...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/195460 |
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| _version_ | 1841524658854166528 |
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| author | Jun Guo Guozheng Yan Mingjian Cai |
| author_facet | Jun Guo Guozheng Yan Mingjian Cai |
| author_sort | Jun Guo |
| collection | DOAJ |
| description | This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (μ, λ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method. |
| format | Article |
| id | doaj-art-b65c16d4e1504d8eaa8b65ad5c222aef |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b65c16d4e1504d8eaa8b65ad5c222aef2025-02-03T05:47:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/195460195460Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the CoreJun Guo0Guozheng Yan1Mingjian Cai2School of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, ChinaSchool of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, ChinaThis paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (μ, λ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method.http://dx.doi.org/10.1155/2015/195460 |
| spellingShingle | Jun Guo Guozheng Yan Mingjian Cai Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core Journal of Applied Mathematics |
| title | Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core |
| title_full | Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core |
| title_fullStr | Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core |
| title_full_unstemmed | Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core |
| title_short | Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core |
| title_sort | multilayered scattering problem with generalized impedance boundary condition on the core |
| url | http://dx.doi.org/10.1155/2015/195460 |
| work_keys_str_mv | AT junguo multilayeredscatteringproblemwithgeneralizedimpedanceboundaryconditiononthecore AT guozhengyan multilayeredscatteringproblemwithgeneralizedimpedanceboundaryconditiononthecore AT mingjiancai multilayeredscatteringproblemwithgeneralizedimpedanceboundaryconditiononthecore |