Türker Özsarı

Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line

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 Schrodinger 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.

Finite-parameter feedback control for stabilizing the complex Ginzburg–Landau equation

In this paper, we prove the exponential stabilization of solutions for complex Ginzburg-Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg-Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.