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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.15911 |
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| _version_ | 1866914607643230208 |
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| author | Bhattacharyya, Sombuddha Kumar, Pranav |
| author_facet | Bhattacharyya, Sombuddha Kumar, Pranav |
| contents | In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and boundary data in suitable function spaces. In the inverse problem, we prove uniqueness of the lower order time-dependent perturbations from the partial input-output operator. The restriction in the measurements are considered by restricting some of the Neumann data over a portion of the lateral boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data Bhattacharyya, Sombuddha Kumar, Pranav Analysis of PDEs 35R30, 35L05, 35L25, 35L35 In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and boundary data in suitable function spaces. In the inverse problem, we prove uniqueness of the lower order time-dependent perturbations from the partial input-output operator. The restriction in the measurements are considered by restricting some of the Neumann data over a portion of the lateral boundary. |
| title | Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data |
| topic | Analysis of PDEs 35R30, 35L05, 35L25, 35L35 |
| url | https://arxiv.org/abs/2504.15911 |