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Control from an interior hypersurface

Galkowski, J; Leautaud, M; (2020) Control from an interior hypersurface. Transactions Of The American Mathematical Society , 373 (5) pp. 3177-3233. 10.1090/tran/7938. Green open access

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Abstract

We consider a compact Riemannian manifold M (possibly with boundary) and Σ ⊂ M \ ∂M an interior hypersurface (possibly with boundary). We study observation and control from Σ for both the wave and heat equations. For the wave equation, we prove controllability from Σ in time T under the assumption (T GCC) that all generalized bicharacteristics intersect Σ transversally in the time interval (0, T). For the heat equation we prove unconditional controllability from Σ. As a result, we obtain uniform lower bounds for the Cauchy data of Laplace eigenfunctions on Σ under T GCC and unconditional exponential lower bounds on such Cauchy data.

Type: Article
Title: Control from an interior hypersurface
Open access status: An open access version is available from UCL Discovery
DOI: 10.1090/tran/7938
Publisher version: https://doi.org/10.1090/tran/7938
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
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/10096945
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