Browsing Matematik by Author "Gürel, Burak."

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  • A mathematical model of drug delivery by modifying the tumor microenvironment: MMP activation 
    Kaba, Duygu. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    Cancer modeling has become one of the challenging frontiers of applied mathematics mostly for two decades. Drug delivery to solid tumors also attracts both theorists and experimentalists due to its signi cance in cancer ...
  • Algebro-geometric solutions of the kadomtsev-petviashvili equation 
    Çiçek, Fatma. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2014., 2014.)
    I. M. Krichever suggested a method to solve nonlinear partial di erential equations in the form of the Zaharov-Shabat Equation [L {u100000} @y;A {u100000} @t] = 0 where L and A are di erential operators including derivatives ...
  • Global well-posedness of NLS equations 
    Yılmaz, Oğuz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)
    The thesis is a survey of the I-method. After introducing the method, we discuss the implementation of this method to cubic, defocusing nonlinear Schrödinger equation in the spatial dimension n = 2 and quintic, defocusing ...
  • Mackey functors and fusion systems 
    İplikçi, Ayçin. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we present a survey for the paper [1]. We study with the biset functors representation rings and superclass functions. We define representation rings of a saturated fusion system F and F-stable elements of ...
  • Null controllability of 1-d heat equation with switching controls 
    Taghiyev, Ali. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.)
    In [1], Zuazua analyzed the problem of two switching controls for null controllability of the 1-d heat equation with Dirichlet's boundary conditions and obtained su cient conditions for null controls satisfying switching ...
  • On special solutions of Zakharov-Schulman equations 
    Bilman, Deniz. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.)
    In this work, two types of special solutions for Zakharov–Schulman equations are studied. Existence of standing wave solutions are established by utilizing variational methods. First set conditions on the operators for the ...
  • On the integrability of the generalized Davey-Stewartson system 
    Çolak, İlker Evrim. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.)
    A method developed by V. E. Zakharov and E. I. Shul'man for understanding the integrable cases of a given system of di erential equations having some certain Hamiltonian structure is represented. Then an application of ...
  • Smoothing estimates for the periodic KdV equation 
    Kuzgun, Şefika. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.)
    In this thesis we aim at understanding an article of M. B. Erdo gan and N. Tzirakis on the famous KdV (Korteweg-de Vries) equation, entitled \Global smoothing for the periodic KdV", which appeared in International Mathematics ...
  • Smoothing properties of initial-boundary value problems 
    Başakoğlu, Engin. (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)
    This thesis discusses the smoothing properties of dispersive partial differential equations. In the first part of the thesis, we consider the Davey–Stewartson system on R 2 and demonstrate that the nonlinear part of the ...
  • Traces of operators with integrable kernels 
    Başakoğlu, Engin. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.)
    Trace class operators are compact operators whose singular values are absolutely summable. C. Brislawn proved in [1] and [2] that a trace formula for trace class operator on L2(X) is determined by it's corresponding kernel ...

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