Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Subject: search.filters.subject.Nonlinear boundary conditions

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  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Blow-Up of Solutions of Nonlinear Schrödinger Equations With Oscillating Nonlinearities
    (American Institute of Mathematical Sciences, 2019) Özsarı, Türker; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    The 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: 13
    Citation - Scopus: 14
    Nonlinear Schrödinger Equations on the Half-Line With Nonlinear Boundary Conditions
    (Texas State University - San Marcos, 2016) Batal, Ahmet; Özsarı, Türker; Batal, Ahmet; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In 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.