Control and Stabilization of the Nonlinear Schroedinger Equation on Rectangles - Archive ouverte HAL Access content directly
Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2010

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.
Fichier principal
Vignette du fichier
rect-soum.pdf (457.56 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00453074 , version 1 (03-02-2010)

Identifiers

Cite

Lionel Rosier, Bing-Yu Zhang. Control and Stabilization of the Nonlinear Schroedinger Equation on Rectangles. Mathematical Models and Methods in Applied Sciences, 2010, 20 (12), pp.2293-2347. ⟨10.1142/S0218202510004933⟩. ⟨hal-00453074⟩
116 View
194 Download

Altmetric

Share

Gmail Facebook X LinkedIn More