Kian, Y;
Kurylev, Y;
Lassas, M;
Oksanen, L;
(2019)
Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets.
Journal of Differential Equations
, 267
(4)
pp. 2210-2238.
10.1016/j.jde.2019.03.008.
Preview |
Text
disjoint_revision_2018_12m_01d.pdf - Accepted Version Download (576kB) | Preview |
Abstract
We consider a restricted Dirichlet-to-Neumann map Λ S,RT associated with the operator ∂ t2 −Δ g +A+q where Δ g is the Laplace-Beltrami operator of a Riemannian manifold (M,g), and A and q are a vector field and a function on M. The restriction Λ S,RT corresponds to the case where the Dirichlet traces are supported on (0,T)×S and the Neumann traces are restricted on (0,T)×R. Here S and R are open sets, which may be disjoint, on the boundary of M. We show that Λ S,RT determines uniquely, up the natural gauge invariance, the lower order terms A and q in a neighborhood of the set R assuming that R is strictly convex and that the wave equation is exactly controllable from S in time T/2. We give also a global result under a convex foliation condition. The main novelty is the recovery of A and q when the sets R and S are disjoint. We allow A and q to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy.
Type: | Article |
---|---|
Title: | Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1016/j.jde.2019.03.008 |
Publisher version: | https://doi.org/10.1016/j.jde.2019.03.008 |
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, Partial data |
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.ucl.ac.uk/id/eprint/10072538 |
Archive Staff Only
View Item |