18 citations · 19 across the 6 of their papers we have counts for
9 papers
Local well-posedness of the higher-order nonlinear Schrödinger equation on the half-line: the case of two boundary conditions
Aykut Alkın, Dionyssios Mantzavinos, Türker Özsarı
We prove the local Hadamard well-posedness of the higher-order nonlinear Schrödinger equation with negative dispersion coefficient on the half-line under nonzero Dirichlet and Neum…
A new approach for the analysis of evolution partial differential equations on a finite interval
Türker Özsarı, Dionyssios Mantzavinos, Konstantinos Kalimeris
We show that, for certain evolution partial differential equations, the solution on a finite interval can be reconstructed as a superposition of restrictions to $(0,\ell…
Well-posedness of the higher-order nonlinear Schrödinger equation on a finite interval
Chris Mayo, Dionyssios Mantzavinos, Türker Ozsarı
We establish the local Hadamard well-posedness of a certain third-order nonlinear Schrödinger equation with a multi-term linear part and a general power nonlinearity known as the h…
Finite dimensional backstepping controller design
Varga Kalantarov, Türker Özsarı, Kemal Cem Yılmaz
We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier mod…
Local well-posedness of the higher order nonlinear Schrödinger equation on the half-line: single boundary condition case
Aykut Alkın, Dionyssios Mantzavinos, Türker Özsarı
We establish local well-posedness for the higher-order nonlinear Schrödinger equation, formulated on the half-line. We consider the scenario of associated coefficients such that on…
Fokas method for linear boundary value problems involving mixed spatial derivatives
Ahmet Batal, Athanassios S. Fokas, Türker Özsarı
We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified trans…
Pseudo-backstepping and its application to the control of Korteweg-de Vries equation from the right endpoint on a finite domain
Türker Özsarı, Ahmet Batal
In this paper, we design Dirichlet-Neumann boundary feedback controllers for the Korteweg-de Vries (KdV) equation that act at the right endpoint of the domain. The length of the do…
Blow-up of solutions of nonlinear Schrödinger equations with oscillating nonlinearities
Türker Özsarı
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 interi…
Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line
Varga K. Kalantarov, Türker Özsarı
In 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 Schrö…