Global controllability and stabilization for the nonlinear Schrodinger equation on an interval

Camille Laurent (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near $0$. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.

Mots clés: Controllability; Stabilization; Nonlinear Schrödinger equation Bourgain spaces

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Camille Laurent. Global controllability and stabilization for the nonlinear Schrodinger equation on an interval. 2008. ⟨hal-00281950⟩