8 papers
Exponential stability for the nonlinear Schrödinger equation on a star-shaped network
Kaïs Ammari, Ahmed Bchatnia, Naima Mehenaoui
In this paper, we prove the exponential stability of the solution of the nonlinear dissipative Schrödinger equation on a star-shaped network and where the damping is localized on o…
Decay of the local energy for the solutions of the critical Klein-Gordon equation
Ahmed Bchatnia, Naima Mehenaoui
In this paper, we prove the exponential decay of local energy for the Klein-Gordon equation with localized critical nonlinearity. The proof relies on generalized Strichartz estimat…
Stabilization of the wave equation with moving boundary
Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti
We deal with the wave equation with assigned moving boundary () upon which Dirichlet-Neuman boundary conditions are satisfied, here is assumed to move slower than…
Improved results on the nonlinear feedback stabilization of a rotating body-beam system
K. Ammari, A. Bchatnia, B. Chentouf
This article is dedicated to the investigation of the stabilization problem of a flexible beam attached to the center of a rotating disk. We assume that the feedback law contains a…
Non uniform decay of the energy of some dissipative evolution systems
Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observabil…
A remark on observability of the wave equation with moving boundary
K. Ammari, A. Bchatnia, K. El Mufti
We deal with the wave equation with assigned moving boundary () upon which Dirichlet or mixed boundary conditions are specified, here is assumed to move slower tha…
Stabilization of the nonlinear damped wave equation via linear weak observability
K. Ammari, A. Bchatnia, K. El Mufti
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an i…
Local energy decay for the wave equation with nonlinear time dependent damping
A. Bchatnia, M. Daoulatli
This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay…