Yazar "Cavalcanti, Marcelo M." seçeneğine göre listele

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    Exponential stability for the nonlinear Schrödinger equation with locally distributed damping
    (Maltepe Üniversitesi, 2019) Cavalcanti, Marcelo M.; Correa, Wellington J.; Özsarı, Turker; Sepulveda, Mauricio; Vejar Asem, Rodrigo
    This talk is concerned with the defocusing nonlinear Schr¨odinger equation with a locally distributed damping on a smooth bounded domain. We first construct approximate solutions for this model by using the theory of monotone operators. We show that these approximate solutions decay exponentially fast in the L 2 -sense by using the multiplier technique and a unique continuation property. Then, we prove the global existence as well as the L 2 -decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. Finally, we implement a precise and efficient algorithm for studying the exponential decay established in the first part of the paper numerically. Our simulations illustrate the efficacy of the proposed control design.
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    Uniform stabilization of the Klein-Gordon system
    (Maltepe Üniversitesi, 2019) Cavalcanti, Marcelo M.
    We consider the Klein-Gordon system posed in an inhomogeneous medium ? with smooth boundary ?? subject to two localized dampings. The first one is of the type viscoelastic and is distributed around a neighborhood ? of the boundary according to the Geometric Control Condition. The second one is a frictional damping and we consider it hurting the geometric condition of control. We show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space. For this purpose, refined microlocal analysis arguments are considered by exploiting ideas due to Burq and Gérard [3].