Feizmohammadi, A;
Kian, Y;
(2019)
Recovery of Nonsmooth Coefficients Appearing in Anisotropic Wave Equations.
SIAM Journal on Mathematical Analysis
, 51
(6)
pp. 4953-4976.
10.1137/19M1251394.
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Abstract
We study the problem of unique recovery of a nonsmooth one-form $\mathcal{A}$ and a scalar function $q$ from the Dirichlet to Neumann map, $\Lambda_{\mathcal{A},q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We prove uniqueness of the one-form $\mathcal{A}$ up to the natural gauge, under weak regularity conditions on $\mathcal{A},q$ and under the assumption that $(M,g)$ is simple. Under an additional regularity assumption, we also derive uniqueness of the scalar function $q$. The proof is based on the geometric optic construction and inversion of the light ray transform extended as a Fourier integral operator to nonsmooth parameters and functions.
| Type: | Article |
|---|---|
| Title: | Recovery of Nonsmooth Coefficients Appearing in Anisotropic Wave Equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/19M1251394 |
| Publisher version: | https://doi.org/10.1137/19M1251394 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse problems, Dirichlet to Neumann map, nonsmooth parameters, light ray transform, time-dependent coefficients, simple manifolds, magnetic potential |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10107001 |
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