Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909267822379008 |
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| author | Liu, Boya Saksala, Teemu Yan, Lili |
| author_facet | Liu, Boya Saksala, Teemu Yan, Lili |
| contents | We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in other words, compact Riemannian manifolds with boundary conformally embedded in a product of the Euclidean line and a transversal manifold. With an additional assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove that the knowledge of a certain partial Cauchy data set determines time-dependent damping coefficient and potential uniquely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10442 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential Liu, Boya Saksala, Teemu Yan, Lili Analysis of PDEs 35R30, 35L05, 58J45 We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in other words, compact Riemannian manifolds with boundary conformally embedded in a product of the Euclidean line and a transversal manifold. With an additional assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove that the knowledge of a certain partial Cauchy data set determines time-dependent damping coefficient and potential uniquely. |
| title | Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential |
| topic | Analysis of PDEs 35R30, 35L05, 58J45 |
| url | https://arxiv.org/abs/2306.10442 |