Bosi, R;
Kurylev, Y;
Lassas, M;
(2016)
Stability of the unique continuation for the wave operator via Tataru inequality and applications.
Journal of Differential Equations
, 260
(8)
pp. 6451-6492.
10.1016/j.jde.2015.12.043.
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Abstract
In this paper we study the stability of the unique continuation in the case of the wave equation with variable coefficients independent of time. We prove a logarithmic estimate in an arbitrary domain of Rn+1, where all the parameters are calculated explicitly in terms of the C1-norm of the coefficients and on the other geometric properties of the problem. We use the Carleman-type estimate proved by Tataru in 1995 and an iteration of the local stability. We apply the result to the case of a wave equation with data on a cylinder and we get a stable estimate for any positive time, also after the first conjugate point associated with the geodesics of the metric of the variable coefficients.
Type: | Article |
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Title: | Stability of the unique continuation for the wave operator via Tataru inequality and applications |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1016/j.jde.2015.12.043 |
Publisher version: | http://dx.doi.org/10.1016/j.jde.2015.12.043 |
Language: | English |
Additional information: | Copyright © 2016. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0. |
Keywords: | Wave equation, Unique continuation property, Stability, Analysis on manifolds, Optimal control time |
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 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/1478784 |
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