Kian, Y;
Oksanen, L;
(2019)
Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations.
International Mathematics Research Notices
, 2019
(16)
pp. 5087-5126.
10.1093/imrn/rnx263.
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Abstract
Given (M,g), a compact connected Riemannian manifold of dimension d≥2, with boundary ∂M, we study the inverse boundary value problem of determining a time-dependent potential q, appearing in the wave equation ∂2tu−Δgu+q(t,x)u=0 in M¯¯¯¯¯=(0,T)×M with T>0. Under suitable geometric assumptions we prove global unique determination of q∈L∞(M¯¯¯¯¯) given the Cauchy data set on the whole boundary ∂M¯¯¯¯¯, or on certain subsets of ∂M¯¯¯¯¯. Our problem can be seen as an analogue of the Calderón problem on the Lorentzian manifold (M¯¯¯¯¯,dt2−g).
| Type: | Article |
|---|---|
| Title: | Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnx263 |
| Publisher version: | https://doi.org/10.1093/imrn/rnx263 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse problems, wave equation on manifold, time-dependent potential, uniqueness, partial data, Carleman estimates |
| 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/10086872 |
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