Stabilisation pour l'Équation des Ondes dans un Domaine Extérieur

Smoothing effect for regularized Schrödinger equation on compact manifolds

“…Under a microlocal geometric assumption called "geometric control", J. Rauch and M. Taylor [16] proved the uniform energy decay for the dissipative wave equation on compact manifold (where all rays are captive). This result was extended to the case of manifolds with boundary by C. Bardos, G. Lebeau and J. Rauch [2] (see [1] for exterior domain).…”

Local Energy Decay for Linear Wave Equations with Localized Dissipation

“…The analogous of our problem for compactly supported data case has been discussed in the works of Aloui-Khénissi [1] and Khénissi [7] through the microlocal analysis under the so called exterior geometric control assumption. Their works are inspired from the famous paper due to Bardos-Lebeau-Rauch [2].…”

“…The author would like to thank the referee who pointed out important references [1], [2] and [7], which were missing in the first version of this paper.…”

Stabilization of Schrödinger equation in exterior domains

“…One can easily show that A a is maximal dissipative (same proof as [1], Prop. 4.1); according then to the Hille-Yoshida theorem, it generates a semi group of contractions…”

“…For the wave equation in odd space dimension, Aloui and Khenissi [1] introduce a damping term of type a(x)∂ t u (a ≥ 0); assuming then the E.G.C. (Exterior Geometric Control) condition on the couple (ω = {a(x) > 0} , T ) for some T > 0, they prove a stabilization result.…”