On uniqueness of inverse conductive scattering problem with unknown embedded obstacles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914257855053824 |
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| author | Wu, Chengyu Yang, Jiaqing |
| author_facet | Wu, Chengyu Yang, Jiaqing |
| contents | This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by the fixed frequency far-field measurements, ignoring its contents. Meanwhile, the boundary informations of several related physical coefficients are also uniquely determined. The proof is mainly based on a detailed singularity analysis of solutions near the interface associated with a family of point sources or hypersingular point sources, which is deduced by the potential theory. Moreover, the other key ingredient in the proof is the well-posedness of the interior transmission problem with the conductivity boundary condition in the L^2 sense, where several sufficient conditions depending on the domain and physical coefficients are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On uniqueness of inverse conductive scattering problem with unknown embedded obstacles Wu, Chengyu Yang, Jiaqing Analysis of PDEs 35R30 This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by the fixed frequency far-field measurements, ignoring its contents. Meanwhile, the boundary informations of several related physical coefficients are also uniquely determined. The proof is mainly based on a detailed singularity analysis of solutions near the interface associated with a family of point sources or hypersingular point sources, which is deduced by the potential theory. Moreover, the other key ingredient in the proof is the well-posedness of the interior transmission problem with the conductivity boundary condition in the L^2 sense, where several sufficient conditions depending on the domain and physical coefficients are provided. |
| title | On uniqueness of inverse conductive scattering problem with unknown embedded obstacles |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2412.12452 |