Stabilization of the wave equation with moving boundary

Abstract : We deal with the wave equation with assigned moving boundary (0 < x < a(t)) upon which DirichletNeuman boundary conditions are satisfied, here a(t) is assumed to move slower than light and periodically. We give a feedback which guarantees the exponential decay of the energy. The proof relies on a reduction theorem by Ammari et al. (2017) [1] and Yoccoz (1984) [13]. At the end we give a remark on the moving-pointwise stabilization problem. (C) 2017 European Control Association. Published by Elsevier Ltd. All rights reserved.
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Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti. Stabilization of the wave equation with moving boundary. European Journal of Control, Lavoisier, 2018, 39, pp.35-38. ⟨10.1016/j.ejcon.2017.10.004⟩. ⟨hal-02169452⟩

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