Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Institution Author: search.filters.institutionAuthor.Özsarı, TürkerPublisher: search.filters.publisher.Taylor and Francis Ltd.

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  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Exponential Stability for the Nonlinear Schrodinger Equation With Locally Distributed Damping
    (Taylor and Francis Ltd., 2020) Cavalcanti, Marcelo M.; Özsarı, Türker; Özsarı, Türker; Sepulveda, Mauricio; Vejar-Aseme, Rodrigo; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Boosting the Decay of Solutions of the Linearised Korteweg-De Vries–burgers Equation To a Predetermined Rate From the Boundary
    (Taylor and Francis Ltd., 2019) Özsarı, Türker; Özsarı, Türker; Arabacı, Eda; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    The aim of this article is to extend recent results on the boundary feedback controllability of the Korteweg-de Vries equation to the Korteweg-de Vries–Burgers equation which is posed on a bounded domain. In the first part of the paper, it is proven that all the sufficiently small solutions can be steered to zero at any desired exponential rate by means of a suitably constructed boundary feedback controller. In the second part, an observer is proposed when a type of boundary measurement is available while there is no full access to the medium.