Recovery of time dependent coefficients from boundary data for hyperbolic equations
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.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
European Mathematical Society - EMS - Publishing House GmbH
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202309115062Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1664-039X
DOI
https://doi.org/10.4171/jst/367
Language
English
Published in
Journal of Spectral Theory
Citation
- Feizmohammadi, A., Ilmavirta, J., Kian, Y., & Oksanen, L. (2021). Recovery of time dependent coefficients from boundary data for hyperbolic equations. Journal of Spectral Theory, 11(3), 1107-1143. https://doi.org/10.4171/jst/367
License
Copyright© 2021 European Mathematical Society. Published by EMS Press.