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• W1974321114 abstract "Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality method proposed by Fursikov and Imanuvilov in the context of parabolic equations, we propose a constructive method to derive controls that weakly depend on the potentials. The second application concerns an inverse problem for the waves that consists in recovering an unknown time-independent potential from a single measurement of the flux. In that context, our approach does not yield any new stability result, but proposes a constructive algorithm to rebuild the potential. In both cases, the main idea is to introduce weighted functionals that contain the Carleman weights and then to take advantage of the freedom on the Carleman parameters to limit the influences of the potentials. Keywords: Carleman estimatesControllabilityInverse problemReconstructionWave equationAMS Subject Classification: 93B0793C2035R30 Acknowledgments The authors thank Jean-Pierre Puel and Belhassen Dehman for their encouragements concerning that work. The authors also wish to thank Institut Henri Poincaré (Paris, France) for providing a very stimulating environment during the “Control of Partial and Differential Equations and Application” program in the Fall 2010. This research was partially supported by the Agence Nationale de la Recherche (ANR, France), Project CISIFS number NT09-437023 and the University Paul Sabatier (Toulouse 3), AO PICAN." @default.
• W1974321114 created "2016-06-24" @default.
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• W1974321114 date "2013-05-04" @default.
• W1974321114 modified "2023-10-17" @default.
• W1974321114 title "Global Carleman Estimates for Waves and Applications" @default.
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• W1974321114 doi "https://doi.org/10.1080/03605302.2013.771659" @default.
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