Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929551921119232 |
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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 potential appearing in the wave equation in conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that are conformally embedded in a product of the real line and a transversal manifold. Under the assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove the unique determination of time-dependent potentials from the knowledge of a certain partial Cauchy data set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09845 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds Liu, Boya Saksala, Teemu Yan, Lili Analysis of PDEs 35R30, 35L05, 58J45 We study an inverse problem of determining a time-dependent potential appearing in the wave equation in conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that are conformally embedded in a product of the real line and a transversal manifold. Under the assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove the unique determination of time-dependent potentials from the knowledge of a certain partial Cauchy data set. |
| title | Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds |
| topic | Analysis of PDEs 35R30, 35L05, 58J45 |
| url | https://arxiv.org/abs/2309.09845 |