Mathematics / Matematik

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

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Author: search.filters.author.Kalimeris, KonstantinosSubject: search.filters.subject.Fokas method

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  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Dispersion Estimates for the Boundary Integral Operator Associated With the Fourth Order Schrödinger Equation Posed on the Half Line
    (Element d.o.o., 2022) Özsarı, Türker; Alkan, Kıvılcım; Kalimeris, Konstantinos
    In this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr¨odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally require highly technical approaches, as opposed to our simple treatment which is based on constructing a boundary integral operator of oscillatory nature via the Fokas method. Our method is uniform and can be extended to other higher order partial differential equations where the main equation possibly involves more than one spatial derivatives.
  • Article
    Citation - WoS: 26
    Citation - Scopus: 27
    An Elementary Proof of the Lack of Null Controllability for the Heat Equation on the Half Line
    (Elsevier, 2020) Kalimeris, Konstantinos; Özsarı, Türker
    In 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.