by Ali Feizmohammadi, Joonas Ilmavirta, Yavar Kian, Lauri Oksanen
Abstract:
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
Reference:
Recovery of time dependent coefficients from boundary data for hyperbolic equations (Ali Feizmohammadi, Joonas Ilmavirta, Yavar Kian, Lauri Oksanen), Journal of Spectral Theory, volume 11, number 3, pp. 1107–1143, 2021.
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We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
[arXiv]
Bibtex Entry:
@article{t-dep-wave,
author = {Ali Feizmohammadi and Joonas Ilmavirta and Yavar Kian and Lauri Oksanen},
title = {{Recovery of time dependent coefficients from boundary data for hyperbolic equations}},
journal = {Journal of Spectral Theory},
volume = 11,
number = 3,
pages = {1107--1143},
month = aug,
year = {2021},
doi = {10.4171/JST/367},
arxiv = {1901.04211},
url={http://users.jyu.fi/~jojapeil/pub/t-dep-wave.pdf},
gsid = {15620981458882392900},
abstract = {We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.},
doi = {10.4171/jst/367}
}