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Stabilization of the wave equations with localized Kelvin–Voigt type damping under optimal geometric conditions

Abstract : The purpose of this note is to investigate the stabilization of the wave equation with Kelvin–Voigt damping in a bounded domain. Damping is localized via a non-smooth coefficient in a suitable subdomain. We prove a polynomial stability result in any space dimension, provided that the damping region satisfies some geometric conditions. The main novelty of this note is that the geometric situations covered here are richer than that considered in [25], [22], [16] and include in particular an example where the damping region is not localized in a neighborhood of the whole or a part of the boundary.
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Submitted on : Wednesday, June 24, 2020 - 12:56:11 PM
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Rayan Nasser, Nahla Noun, Ali Wehbe. Stabilization of the wave equations with localized Kelvin–Voigt type damping under optimal geometric conditions. Comptes Rendus Mathématique, Elsevier Masson, 2019, 357 (3), pp.272-277. ⟨10.1016/j.crma.2019.01.005⟩. ⟨hal-02098422⟩

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