I am a faculty member at the Mathematics Department of Bilkent University. I received my PhD in Mathematics from the University of Virginia. I got my MS in Mathematics and my BS degrees in Mathematics and Computer Engineering from Koç University. I have held positions at Doğuş University, UNC-Charlotte, and IZTECH. I was also a visiting faculty at the University of Cambridge.
My research fields are analysis of partial differential equations and control theory. I have a particular interest in the design, analysis, and controllability of initial-boundary value problems (IBVPs) which define spatio-temporal phenomena in applied sciences. My goal is to understand and change the qualitative behavior of solutions of such IBVPs. The latter is achieved by designing a suitable control system which drives solutions to or near a desired state, possibly in long time.
I have written research articles on the analysis and control of various fundamental physical PDEs including the nonlinear Schrödinger equation (NLS), biharmonic NLS, higher order NLS, complex Ginzburg-Landau equation (CGLE), Korteweg de-Vries (KdV) equation, KdV-Burgers equation, and the heat equation.
Here are a few selected articles of mine (for a full list of publications click here):
- 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
- 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
- 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