Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential

2023/06/18 by Boya Liu, Liu, Boya, Teemu Saksala +3 · 3 citations
Computer Science · Mathematics · #35L05 #35R30 #58J45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2306.10442

openalex publication_date 2023/06/18 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

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.

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• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
• A Hyperbolic Inverse Problem for lower order terms on a closed manifold with disjoint data
• Hölder stability of an inverse spectral problem for the magnetic Schrödinger operator on a simple manifold

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