Uniform observability estimates for linear waves
Identifieur interne : 000003 ( Main/Exploration ); précédent : 000002; suivant : 000004Uniform observability estimates for linear waves
Auteurs : Camille Laurent [France] ; Matthieu Léautaud [France]Source :
- ESAIM: Control, Optimisation and Calculus of Variations [ 1292-8119 ] ; 2016-10-21.
Abstract
In this article, we give a completely constructive proof of the observability/controllability of the wave equation on a compact manifold under optimal geometric conditions. This contrasts with the original proof of Bardos–Lebeau–Rauch [C. Bardos, G. Lebeau and J. Rauch, SIAM J. Control Optim. 30 (1992) 1024–1065], which contains two non-constructive arguments. Our method is based on the Dehman-Lebeau [B. Dehman and G. Lebeau, SIAM J. Control Optim. 48 (2009) 521–550] Egorov approach to treat the high-frequencies, and the optimal unique continuation stability result of the authors [C. Laurent and M. Léautaud. Preprint arXiv:1506.04254 (2015)] for the low-frequencies. As an application, we first give estimates of the blowup of the observability constant when the time tends to the limit geometric control time (for wave equations with possibly lower order terms). Second, we provide (on manifolds with or without boundary) with an explicit dependence of the observability constant with respect to the addition of a bounded potential to the equation.
Url:
DOI: 10.1051/cocv/2016046
Affiliations:
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This contrasts with the original proof of Bardos–Lebeau–Rauch [C. Bardos, G. Lebeau and J. Rauch, SIAM J. Control Optim. 30 (1992) 1024–1065], which contains two non-constructive arguments. Our method is based on the Dehman-Lebeau [B. Dehman and G. Lebeau, SIAM J. Control Optim. 48 (2009) 521–550] Egorov approach to treat the high-frequencies, and the optimal unique continuation stability result of the authors [C. Laurent and M. Léautaud. Preprint arXiv:1506.04254 (2015)] for the low-frequencies. As an application, we first give estimates of the blowup of the observability constant when the time tends to the limit geometric control time (for wave equations with possibly lower order terms). Second, we provide (on manifolds with or without boundary) with an explicit dependence of the observability constant with respect to the addition of a bounded potential to the equation.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Laurent, Camille" sort="Laurent, Camille" uniqKey="Laurent C" first="Camille" last="Laurent">Camille Laurent</name></region><name sortKey="Leautaud, Matthieu" sort="Leautaud, Matthieu" uniqKey="Leautaud M" first="Matthieu" last="Léautaud">Matthieu Léautaud</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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