Recovery of time-dependent coefficients from boundary data for hyperbolic equations

  • Ali Feizmohammadi

    The Fields Institute for Research in Mathematical Sciences, Toronto, Canada
  • Joonas Ilmavirta

    University of Jyväskylä, Finland
  • Yavar Kian

    Aix Marseille Université, Marseille, France
  • Lauri Oksanen

    University of Helsinki, Finland
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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.

Cite this article

Ali Feizmohammadi, Joonas Ilmavirta, Yavar Kian, Lauri Oksanen, Recovery of time-dependent coefficients from boundary data for hyperbolic equations. J. Spectr. Theory 11 (2021), no. 3, pp. 1107–1143

DOI 10.4171/JST/367