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 L2. We also get a regularity result about the control if the data are assumed smoother.
Keywords: controllability, stabilization, nonlinear Schrödinger equation, Bourgain spaces
@article{COCV_2010__16_2_356_0, author = {Laurent, Camille}, title = {Global controllability and stabilization for the nonlinear {Schr\"odinger} equation on an interval}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {356--379}, publisher = {EDP-Sciences}, volume = {16}, number = {2}, year = {2010}, doi = {10.1051/cocv/2009001}, mrnumber = {2654198}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009001/} }
TY - JOUR AU - Laurent, Camille TI - Global controllability and stabilization for the nonlinear Schrödinger equation on an interval JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 356 EP - 379 VL - 16 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009001/ DO - 10.1051/cocv/2009001 LA - en ID - COCV_2010__16_2_356_0 ER -
%0 Journal Article %A Laurent, Camille %T Global controllability and stabilization for the nonlinear Schrödinger equation on an interval %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 356-379 %V 16 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009001/ %R 10.1051/cocv/2009001 %G en %F COCV_2010__16_2_356_0
Laurent, Camille. Global controllability and stabilization for the nonlinear Schrödinger equation on an interval. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 356-379. doi : 10.1051/cocv/2009001. http://archive.numdam.org/articles/10.1051/cocv/2009001/
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