Kurylev, Y;
Lassas, M;
Oksanen, L;
(2017)
Hyperbolic inverse problem with data on disjoint sets.
Inverse Problems
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Abstract
We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and the Neumann traces are restricted on another subset. We show that the restricted Dirichlet-to-Neumann map determines the geometry and the lower order terms in the wave equation, up the natural gauge invariances, along a convex foliation of the manifold. The main novelty is the recovery of the lower order terms when the supports of the Dirichlet traces are disjoint from the set on which the Neumann traces are restricted. We allow the lower order terms to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy.
| Type: | Article |
|---|---|
| Title: | Hyperbolic inverse problem with data on disjoint sets |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://arxiv.org/abs/1602.03626 |
| 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. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1522472 |
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