BAUDOUIN, Lucie; DARDÉ, Jérémi; ERVEDOZA, Sylvain; MERCADO, Alberto

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BAUDOUIN, Lucie
Équipe Méthodes et Algorithmes en Commande [LAAS-MAC]

DARDÉ, Jérémi
Institut de Mathématiques de Toulouse UMR5219 [IMT]

ERVEDOZA, Sylvain
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Mathematical Reports. 2022-01, vol. 24, n° 1-2, p. 59-112

Romanian Academy of Sciences

Résumé en anglais

In this work, we develop a unified strategy which allows to derive observability results for waves in an annulus when the observation is done on the external boundary and under various boundary conditions at the internal boundary. Our approach is based on the fact that the observability of a linear abstract conservative system is equivalent to a suitable resolvent estimate. We develop a full machinery to derive suitable resolvent estimates under some weak assumptions on the boundary condition on the internal sphere, which are shown to be close to sharp. In fact, our strategy allows to exclude the existence of trapped rays close to the internal sphere when the boundary conditions satisfy a suitable assumption. As an application, we apply our results to several wave models.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191263

Project ANR

Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009
Centre International de Mathématiques et d'Informatique (de Toulouse) - ANR-11-LABX-0040

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251