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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…