Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 13Citation - Scopus: 14Nonlinear 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 TechnologyIn 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.Article Citation - WoS: 14Citation - Scopus: 15Qualitative Properties of Solutions for Nonlinear Schrödinger Equations With Nonlinear Boundary Conditions on the Half-Line(American Institute of Physics, 2016) Kalantarov, Varga K.; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a nonlinear defocusing interior source, and a weak damping term for nonlinear Schrödinger equations posed on the infinite half-line. We construct solutions with negative initial energy satisfying a certain set of conditions which blow-up in finite time in the H1-sense. We obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow-up solutions. In addition to the blow-up property, we also discuss the stabilization property and the critical exponent for this model.Article Citation - WoS: 18Citation - Scopus: 19Well-Posedness for Nonlinear Schrödinger Equations With Boundary Forces in Low Dimensions by Strichartz Estimates(Academic Press Inc., 2015) Özsarı, Türker; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this paper, we study the well-posedness of solutions for nonlinear Schrödinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of Dirichlet or Neumann force. We first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the Strichartz estimates on domains. Secondly, we obtain conditional uniqueness and local stability. Then, we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory. Regarding subquadratic sources, we appeal to classical methods and Trudinger's inequality to prove the uniqueness, which, combined with the existence of weak energy solutions, mass and energy inequalities, eventually implies the continuity of solutions in time.