Mathematics / Matematik

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

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Institution Author: search.filters.institutionAuthor.Özsarı, TürkerSubject: search.filters.subject.Unified transform method

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  • Article
    Citation - WoS: 22
    Citation - Scopus: 20
    Fokas Method for Linear Boundary Value Problems Involving Mixed Spatial Derivatives
    (Royal Society of Chemistry, 2020) Fokas, A. S.; Batal, Ahmet; Özsarı, Türker
    We 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 - WoS: 40
    Citation - Scopus: 40
    The Initial-Boundary Value Problem for the Biharmonic Schrödinger Equation on the Half-Line
    (American Institute of Mathematical Sciences, 2019) Özsarı, Türker; Yolcu, Nermin
    We 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.