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

Camille Laurent

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 2, page 356-379
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Laurent, Camille. "Global controllability and stabilization for the nonlinear Schrödinger equation on an interval." ESAIM: Control, Optimisation and Calculus of Variations 16.2 (2010): 356-379. <http://eudml.org/doc/250771>.

@article{Laurent2010,
abstract = { 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. },
author = {Laurent, Camille},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; stabilization; nonlinear Schrödinger equation; Bourgain spaces; controllability},
language = {eng},
month = {4},
number = {2},
pages = {356-379},
publisher = {EDP Sciences},
title = {Global controllability and stabilization for the nonlinear Schrödinger equation on an interval},
url = {http://eudml.org/doc/250771},
volume = {16},
year = {2010},
}

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
DA - 2010/4//
PB - EDP Sciences
VL - 16
IS - 2
SP - 356
EP - 379
AB - 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.
LA - eng
KW - Controllability; stabilization; nonlinear Schrödinger equation; Bourgain spaces; controllability
UR - http://eudml.org/doc/250771
ER -

References

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