Turker Ozsari, University of Virginia


Stabilization of Linear and Nonlinear Schroedinger Equations


Abstract: In this talk, we consider various stabilization problems in the context of both linear and nonlinear Schroedinger equations. We review some well-known results including boundary and interior stabilization problems. Then we present a new result on the stabilization of a weakly damped semilinear Schroedinger equation with inhomogeneous Dirichlet boundary data. We prove that if the boundary data decays (in a physically reasonable sense) then we get the stabilization of the energy. We also remark that the decay rate of the boundary data controls the decay rate of the solutions. Finally, we propose several open problems.

Advisor: Dr. Irena Lasiecka (University of Virginia)