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math.AP2019
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…
math.AP2019
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…
math.AP2015
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…