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Zbl 1217.93032
Laurent, Camille
Global controllability and stabilization for the nonlinear Schrödinger equation on an interval. (English)
[J] ESAIM, Control Optim. Calc. Var. 16, No. 2, 356-379 (2010). ISSN 1292-8119; ISSN 1262-3377/e

Summary: We prove global internal controllability in large time for the nonlinear Schrödinger 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 $L^{2}$. We also get a regularity result about the control if the data are smoother.
MSC 2000:
*93B05 Controllability
93D15 Stabilization of systems by feedback
35Q41
35A21 Propagation of singularities

Keywords: controllability; stabilization; nonlinear Schrödinger equation; Bourgain spaces

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