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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 the time-dependent damping coefficient and potential uniquely.
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This content will become publicly available on March 5, 2026
Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds
We study an inverse problem of determining a time-dependent potential appearing in the wave equation on 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.
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- Award ID(s):
- 2204997
- PAR ID:
- 10645801
- Publisher / Repository:
- European Mathematical Society
- Date Published:
- Journal Name:
- Journal of Spectral Theory
- Volume:
- 15
- Issue:
- 1
- ISSN:
- 1664-039X
- Page Range / eLocation ID:
- 123 to 147
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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