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.
Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti. Stabilization of the wave equation with moving boundary. European Journal of Control, Elsevier, 2018, 39, pp.35-38. ⟨10.1016/j.ejcon.2017.10.004⟩. ⟨hal-02169452⟩