Control and Stabilization of the Nonlinear Schroedinger Equation on Rectangles

Abstract

This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as far as the localization of the control region and the smoothness of the state space are concerned. It is also proved that for the linear Schrödinger equation with Dirichlet control, the exact controllability holds in $H^{-1}(\Omega )$ whenever the control region contains a neighborhood of a vertex.

References in corpus (4)

• On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations
• Some local wellposedness results for nonlinear Schroedinger equations below L^2
• Global controllability and stabilization for the nonlinear Schrödinger equation on some compact manifolds of dimension 3
• Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain