| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 65 | |
| Number of page(s) | 60 | |
| DOI | https://doi.org/10.1051/cocv/2024056 | |
| Published online | 12 September 2024 | |
Control of waves on Lorentzian manifolds with curvature bounds
1
TIFR Centre for Applicable Mathematics Bangalore, 560065, Karnataka, India
2
School of Mathematical Sciences Queen Mary University of London, London E1 4NS, UK
* Corresponding author: vkjena22@tifrbng.res.in
Received:
6
November
2023
Accepted:
29
July
2024
We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds.
Key words: Wave equations / controllability / Carleman estimates / Lorentzian manifolds
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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