Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds

2023/09/18 by Liu, Boya, Saksala, Teemu, Yan, Lili · 2 citations
#35L05 #35R30 #58J45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.09845

Abstract

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.

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