Özsarı, Türker
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Ozsarı, Türker
Özsarı, T.
Özsarı, T
Ozsari, Turker
Ozsari, T.
Ozsari, T
Özsarı, T.
Özsarı, T
Ozsari, Turker
Ozsari, T.
Ozsari, T
Job Title
Email Address
turkerozsari@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
Status
Former Staff
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WoS Researcher ID
Sustainable Development Goals
SDG data is not available
Documents
27
Citations
300
h-index
10
Documents
27
Citations
288
Scholarly Output
26
Articles
20
Views / Downloads
62361/7984
Supervised MSc Theses
3
Supervised PhD Theses
3
WoS Citation Count
214
Scopus Citation Count
212
Patents
0
Projects
5
WoS Citations per Publication
8.23
Scopus Citations per Publication
8.15
Open Access Source
20
Supervised Theses
6
| Journal | Count |
|---|---|
| International Journal of Control | 2 |
| Studies in Applied Mathematics | 2 |
| Communications on Pure and Applied Analysis | 2 |
| Electronic Journal of Differential Equations | 1 |
| Evolution Equations & Control Theory | 1 |
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26 results
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Now showing 1 - 10 of 26
Article Citation - WoS: 3Citation - Scopus: 3Blow-Up of Solutions of Nonlinear Schrödinger Equations With Oscillating Nonlinearities(American Institute of Mathematical Sciences, 2019) Özsarı, TürkerThe finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the nonlinear source is placed at the boundary point. The distinctive feature of this work is that the initial energy is allowed to be non-negative and the momentum is allowed to be infinite in contrast to the previous literature on the blow-up of solutions with time dependent nonlinearities. The common finite momentum assumption is removed by using a compactly supported or rapidly decaying weight function in virial identities - an idea borrowed from [18]. At the end of the paper, a numerical example satisfying the theory is provided.Article Citation - WoS: 13Citation - Scopus: 14Nonlinear Schrödinger Equations on the Half-Line With Nonlinear Boundary Conditions(Texas State University - San Marcos, 2016) Batal, Ahmet; Özsarı, TürkerIn this article, we study the initial boundary value problem for nonlinear Schrödinger equations on the half-line with nonlinear boundary conditions ux(0, t) + λ|u(0, t)|ru(0, t) = 0, λ ∈ ℝ − {0}, r > 0. We discuss the local well-posedness when the initial data u0 = u(x, 0) belongs to an L2-based inhomogeneous Sobolev space (formula presented) with (formula presented). We deal with the nonlinear boundary condition by first studying the linear Schrödinger equation with a time-dependent inhomogeneous Neumann boundary condition ux(0, t) = h(t) where (formula presented) (0, T). © 2016 Texas State University.Doctoral Thesis Boundary Feedback Stabilization of Some Evolutionary Partial Differential Equations(01. Izmir Institute of Technology, 2022) Yılmaz, Kemal Cem; Batal, Ahmet; Özsarı, Türker; Özsarı, Türker; Batal, AhmetThe purpose of this study is to control long time behaviour of solutions to some evolutionary partial differential equations posed on a finite interval by backstepping type controllers. At first we consider right endpoint feedback controller design problem for higher-order Schrödinger equation. The second problem is observer design problem, which has particular importance when measurement across the domain is not available. In this case, the sought after right endpoint control inputs involve state of the observer model. However, it is known that classical backstepping strategy fails for designing right endpoint controllers to higher order evolutionary equations. So regarding these controller and observer design problems, we modify the backstepping strategy in such a way that, the zero equilibrium to the associated closed-loop systems become exponentially stable. From the well-posedness point of view, this modification forces us to obtain a time-space regularity estimate which also requires to reveal some smoothing properties for some associated Cauchy problems and an initial-boundary value problem with inhomogeneous boundary conditions. As a third problem, we introduce a finite dimensional version of backstepping controller design for stabilizing infinite dimensional dissipative systems. More precisely, we design a boundary control input involving projection of the state onto a finite dimensional space, which is still capable of stabilizing zero equilibrium to the associated closed-loop system. Our approach is based on defining the backstepping transformation and introducing the associated target model in a novel way, which is inspired from the finite dimensional long time behaviour of dissipative systems. We apply our strategy in the case of reaction-diffusion equation. However, it serves only as a canonical example and our strategy can be applied to various kind of dissipative evolutionary PDEs and system of evolutionary PDEs. We also present several numerical simulations that support our theoretical results.Article Citation - WoS: 26Citation - Scopus: 27An Elementary Proof of the Lack of Null Controllability for the Heat Equation on the Half Line(Elsevier, 2020) Kalimeris, Konstantinos; Özsarı, TürkerIn this note, we give an elementary proof of the lack of null controllability for the heat equation on the half line by employing the machinery inherited by the unified transform, known also as the Fokas method. This approach also extends in a uniform way to higher dimensions and different initial-boundary value problems governed by the heat equation, suggesting a novel methodology for studying problems related to controllability. (C) 2020 Elsevier Ltd. All rights reserved.Article Stabilisation of Linear Waves With Inhomogeneous Neumann Boundary Conditions(Taylor & Francis Ltd, 2024) Ozsari, Turker; Susuzlu, IdemWe study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of these models presents additional interesting features and challenges compared to their homogeneous counterparts. In the present context, energy depends on the boundary trace of velocity. It is not clear in advance how this quantity should be controlled based on the given data, due to regularity issues. However, we establish global existence and also prove uniform stabilisation of solutions with decay rates characterised by the Neumann input. We supplement these results with numerical simulations in which the data do not necessarily satisfy the given assumptions for decay. These simulations provide, at a numerical level, insights into how energy could possibly change in the presence of, for example, improper data.Article Citation - WoS: 40Citation - Scopus: 40The Initial-Boundary Value Problem for the Biharmonic Schrödinger Equation on the Half-Line(American Institute of Mathematical Sciences, 2019) Özsarı, Türker; Yolcu, NerminWe study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schrodinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for the solution of the linear nonhomogenenous problem by using the Fokas method (also known as the unified transform method). We use this representation formula to prove space and time estimates on the solutions of the linear model in fractional Sobolev spaces by using Fourier analysis. Secondly, we consider the nonlinear model with a power type nonlinearity and prove the local wellposedness by means of a classical contraction argument. We obtain Strichartz estimates to treat the low regularity case by using the oscillatory integral theory directly on the representation formula provided by the Fokas method. Global wellposedness of the defocusing model is established up to cubic nonlinearities by using the multiplier technique and proving hidden trace regularities.Master Thesis Boundary Controller and Observer Design for Korteweg-De Vries Type Equations(Izmir Institute of Technology, 2017) Arabacı, Eda; Özsarı, TürkerThis thesis studies the back-stepping boundary controllability of Korteweg-de Vries (KdV) type equations posed on a bounded interval. The results on the back-stepping controllability of the KdV equation obtained in Cerpa and Coron (2013) and Cerpa (2012) are reviewed and extended to the KdV-Burgers (KdVB) equation. The stability of the KdVB equation is boosted to any desired exponential rate for sufficiently small initial data with a boundary feedback controller acting on the Dirichlet boundary condition. Moreover, the case that there is no full access to the system is considered. For these kinds of systems, an observer is constructed assuming an appropriate boundary measurement is available. The ideas about designing output feedback control for the KdV equation presented in Marx and Cerpa (2016), and Hasan (2016) are reviewed and extended to the KdVB model.Article Citation - WoS: 22Citation - Scopus: 20Fokas Method for Linear Boundary Value Problems Involving Mixed Spatial Derivatives(Royal Society of Chemistry, 2020) Fokas, A. S.; Batal, Ahmet; Özsarı, TürkerWe obtain solution representation formulae for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first implement the method on the second-order parabolic PDEs; in this case one can alternatively eliminate the mixed derivatives by a linear change of variables. Then, we employ the method to biharmonic problems, where it is not possible to eliminate the cross term via a linear change of variables. A basic ingredient of the UTM is the use of certain invariant maps. It is shown here that these maps are well defined provided that certain analyticity issues are appropriately addressed.Article Citation - Scopus: 3Stabilization of Higher Order Schrödinger Equations on a Finite Interval: Part Ii(American Institute of Mathematical Sciences, 2022) Özsarı, Türker; Yılmaz, Kemal CemBackstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [3] where the controller was assumed to be acting from the left endpoint of the medium. In this companion paper, we further the analysis by considering boundary controller(s) acting at the right endpoint of the domain. It turns out that the problem is more challenging in this scenario as the associated boundary value problem for the backstepping kernel becomes overdetermined and lacks a smooth solution. The latter is essential to switch back and forth between the original plant and the so called target system. To overcome this difficulty we rely on the strategy of using an imperfect kernel, namely one of the boundary conditions in kernel PDE model is disregarded. The drawback is that one loses rapid stabilization in comparison with the left endpoint con-trollability. Nevertheless, the exponential decay of the L2-norm with a certain rate still holds. The observer design is associated with new challenges from the point of view of wellposedness and one has to prove smoothing properties for an associated initial boundary value problem with inhomogeneous boundary data. This problem is solved by using Laplace transform in time. However, the Bromwich integral that inverts the transformed solution is associated with certain analyticity issues which are treated through a subtle analysis. Numerical algorithms and simulations verifying the theoretical results are given.Article Citation - WoS: 18Citation - Scopus: 19Well-Posedness for Nonlinear Schrödinger Equations With Boundary Forces in Low Dimensions by Strichartz Estimates(Academic Press Inc., 2015) Özsarı, TürkerIn this paper, we study the well-posedness of solutions for nonlinear Schrödinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of Dirichlet or Neumann force. We first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the Strichartz estimates on domains. Secondly, we obtain conditional uniqueness and local stability. Then, we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory. Regarding subquadratic sources, we appeal to classical methods and Trudinger's inequality to prove the uniqueness, which, combined with the existence of weak energy solutions, mass and energy inequalities, eventually implies the continuity of solutions in time.
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