**Interior-boundary interactions for the nonlinear Schr****ö****dinger and related equations**

**Turker Ozsari **(Izmir Institute of Technology)

**Date/Time: **August 5, 2016- 13.30

**Place: **FENS 2008

**Abstract:** In the first part of my talk, I will discuss the one dimensional Schrödinger equation with nonlinear interior and boundary sources. I will present the local well-posedness result in the fractional Sobolev spaces [*A. Batal & T.Ö., **arXiv:1507.04666, 2016*]. I will also review some results concerning the behavior of solutions: blow-up versus stabilization [*V. Kalantarov & T.O., JMP, 2016*]. I will finish the first part of my talk by giving some recent results concerning the Schrödinger equation with time dependent coefficients (*T.O., revised at EJDE, 2016*).

#### In the second part of my talk, I will review some earlier results on nonlinear Schrödinger equations (NLS) with non-homogeneous boundary interactions pertaining to higher dimensions and energy level. Both Dirichlet [*T.O, V. Kalantarov, I. Lasiecka, JDE, 2011]*, [*T.O, JMAA, 2012*] and Neumann problem [*T.Ö, NA, 2012*] are considered here. Improvements on these results are achieved with the help of Strichartz estimates in low dimensions [*T.O, JMAA, 2014*].

#### In the last part of my talk, if time permits, I will discuss some recent well-posedness results under dynamic/Wentzell boundary conditions on related equations such as the Ginzburg-Landau equation [W.J. Correa *& T.O., preprint*].

**Bio: **Turker Ozsari has been a faculty member in the Mathematics Department of Izmir Institute of Technology (IZTECH) since 2014. He recently established a research group called IZTECH PDE-LAB with the two grants he holds. This group focuses on analysis and control theory of PDEs and currently includes 9 members (2 faculty, 1 postdoc, 2 PhD and 4 MS students). His research is focused on the analysis of nonhomogeneous boundary value problems. He wrote a series of articles on nonlinear Schrödinger equations and a book (with Varga Kalantarov) entitled *Applied Functional Analysis: A PDE Perspective, *to be published by Koc University Press. Prior to his position at IZTECH, he held positions at the University of North Carolina - Charlotte (2013-2014) and Dogus University (2010-2013).

Turker earned his PhD in Mathematics (2010) at the University of Virginia under the direction of Irena Lasiecka. At Koc University, he finished his MS in Mathematics, and his BS in both Mathematics and Computer Engineering. Turker made several invited presentations in well-known institutes, including the University of Memphis and the Johan Radon Institute for Computational and Applied Mathematics. This year he is organizing a *Workshop on Nonlinear PDEs,* to be held from Aug 26 to 28 at IZTECH.