Writings

Preprints

25. Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line (with K. Alkan and K. Kalimeris), submitted, 20 pp. arXiv

24. Numerical computation of Neumann controllers for the heat equation on a finite interval (with K. Kalimeris and N. Dikaios), under review, 19 pp. arXiv

23. The interior-boundary Strichartz estimates for the Schrödinger equation on the half line revisited, 17 pp. arXiv

22. Decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation (with M. M. Cavalcanti, et al.), under review, 46 pp. arXiv

Forthcoming

21. Stabilization of higher order Schrödinger equations on a finite interval: Part II (with K. C. Yılmaz), Evolution Equations and Control Theory, available online (2021), 62 pp. DOI arXiv

Publications

20. Stabilization of higher order Schrödinger equations on a finite interval: Part I (with A. Batal and K. C. Yılmaz), Evolution Equations and Control Theory, 10(4) : 861-919, 2021 DOI arXiv

19. Exponential stability for the nonlinear Schrödinger equation with locally distributed damping (with M. M. Cavalcanti, et al.), Communications in Partial Differential Equations, 45(9), 1134-1167, 2020 DOI arXiv

18. Fokas method for linear boundary value problems involving mixed spatial derivatives (with A. Batal and A. S. Fokas), Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2239), 1-15, 2020. DOI arXiv

17. An elementary proof of the lack of null controllability for the heat equation on the half line (with K. Kalimeris), Applied Mathematics Letters, 104, 106241, 2020 DOI arXiv

16. Output feedback stabilization of the linearized Korteweg-de Vries equation with right endpoint controllers (with A. Batal), Automatica J. IFAC, 109, 108531, 2019 DOI arXiv

15. The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line (with N. Yolcu), Communications on Pure and Applied Analysis, 18(6), 3285-3316, 2019 DOI arXiv

14. New rigorous developments regarding the Fokas method and an open problem (with A.S. Fokas), European Mathematical Society Newsletter, 113, 60-61, 2019 DOI

13. Boosting the decay of solutions of the linearized Korteweg-de Vries-Burgers equation to a predetermined rate from the boundary (with E. Arabacı), International Journal of Control, 92(8), 1753-1763, 2019 DOI

12. Pseudo-backstepping and its application to the control of Korteweg-de Vries equation from the right endpoint on a finite domain (with A. Batal), SIAM Journal on Control and Optimization, 57(2), 1255-1283, 2019 DOI arXiv

11. Blow-up of solutions of nonlinear Schrödinger equations with oscillating nonlinearities, Communications on Pure and Applied Analysis, 18(1), 539-558, 2019 DOI arXiv

10. Complex Ginzburg-Landau equations with dynamic boundary conditions (with W.J. Corrêa), Nonlinear Analysis: Real World Applications, 41, 607-641, 2018 DOI arXiv

09. Finite-parameter feedback control for stabilizing the complex Ginzburg-Landau equation (with J. Kalantarova), Systems & Control Letters, 106, 40-46, 2017 DOI arXiv

08. Nonlinear Schrödinger equations on the half-line with nonlinear boundary conditions (with A. Batal), Electronic Journal of Differential Equations, 2016(222), 1-20, 2016 DOI

07. Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line (with V.K. Kalantarov), Journal of Mathematical Physics, 57(2), 021511, 2016 DOI arXiv

06. Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates, Journal of Mathematical Analysis and Applications, 424(1), 487-508, 2015 DOI

05. Global existence and open loop exponential stabilization of weak solutions for nonlinear Schrödinger equations with localized external Neumann manipulation, Nonlinear Analysis: Theory, Methods & Applications, 80, 179-193, 2013 DOI

04. Weakly-damped focusing nonlinear Schrödinger equations with Dirichlet control, Journal of Mathematical Analysis and Applications, 389(1), 84-97, 2012 DOI

03. Uniform decay rates for the energy of weakly damped defocusing semilinear Schrödinger equations with inhomogeneous Dirichlet boundary control (with V.K. Kalantarov and I. Lasiecka), Journal of Differential Equations, 251(7), 1841-1863, 2011 DOI

02. Stabilization of nonlinear Schrödinger equation with inhomogeneous Dirichlet boundary control, Thesis (Ph.D.)-University of Virginia. 2010. 93 pp.

01. Stabilization of linear and nonlinear Schrödinger equations, Thesis (M.Sc.)-Koç University. 2007. 73 pp.