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Title: Exponential stability for the nonlinear Schrodinger equation with locally distributed damping
Authors: Cavalcanti, Marcelo M.
Correa, Wellington J.
Özsarı, Türker
Sepulveda, Mauricio
Vejar-Aseme, Rodrigo
Keywords: Finite volume method
Locally distributed damping
Monotone operator theory
Nonlinear Schrodinger equation
Unique continuation
Issue Date: 2020
Publisher: Taylor and Francis Ltd.
Abstract: In this paper, we study the defocusing nonlinear Schrodinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using the theory of monotone operators. We show that 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. The distinctive feature of the paper is the monotonicity approach, which makes the analysis independent from the commonly used Strichartz estimates and allows us to work without artificial smoothing terms inserted into the main equation. We in addition 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.
ISSN: 0360-5302
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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