Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

Browse

Filters

2019 - 201912020 - 20231

Settings

COAR Access Rights: search.filters.coarAccessRights.metadata only accessInstitution Author: search.filters.institutionAuthor.Batal, Ahmet

Search Results

Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Irreducibility and Primality in Differentiability Classes
    (Michigan State University Press, 2023) Batal, Ahmet; Eyidoğan, S.; Göral, Haydar
    In this note, we give criteria for the irreducibility of functions in Cm [0, 1], where m ∈ {1, 2, 3, ...} ∪ {∞} ∪ {ω}. We also discuss irreducibility in multivariable differentiability classes. Moreover, we characterize irreducible functions and maximal ideals in C∞ [0, 1]. In fact, irreducible and prime smooth functions are the same, and every maximal ideal of C∞ [0, 1] is principal. © 2023 Michigan State University Press. All rights reserved.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Output Feedback Stabilization of the Linearized Korteweg-De Vries Equation With Right Endpoint Controllers
    (Elsevier Ltd., 2019) Batal, Ahmet; Özsarı, Türker
    In this paper, we prove the output feedback stabilization for the linearized Korteweg-de Vries (KdV) equation posed on a finite domain in the case the full state of the system cannot be measured. We assume that there is a sensor at the left end point of the domain capable of measuring the first and second order boundary traces of the solution. This allows us to design a suitable observer system whose states can be used for constructing boundary feedbacks acting at the right endpoint so that both the observer and the original plant become exponentially stable. Stabilization of the original system is proved in the L-2-sense, while the convergence of the observer system to the original plant is also proved in higher order Sobolev norms. The standard backstepping approach used to construct a left endpoint controller fails and presents mathematical challenges when building right endpoint controllers due to the overdetermined nature of the related kernel models. In order to deal with this difficulty we use the method of Ozsan and Batal, (2019) which is based on using modified target systems involving extra trace terms. In addition, we show that the number of controllers and boundary measurements can be reduced to one, with the cost of a slightly lower exponential rate of decay. We provide numerical simulations illustrating the efficacy of our controllers. (C) 2019 Elsevier Ltd. All rights reserved.