# Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 1, page 277-293
- ISSN: 1292-8119

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topMicu, Sorin, and Rovenţa, Ionel. "Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 277-293. <http://eudml.org/doc/276372>.

@article{Micu2012,

abstract = {This article considers the linear 1-d Schrödinger equation in (0,π)
perturbed by a vanishing viscosity term depending on a small parameter
ε > 0. We study the boundary controllability properties of this
perturbed equation and the behavior of its boundary controls
vε as ε goes to zero. It
is shown that, for any time T sufficiently large but independent of
ε and for each initial datum in
H−1(0,π), there exists a uniformly bounded
family of controls
(vε)ε in
L2(0, T) acting on the extremity
x = π. Any weak limit of this family is a control for
the Schrödinger equation. },

author = {Micu, Sorin, Rovenţa, Ionel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Null-controllability; Schrödinger equation; complex Ginzburg-Landau equation; moment problem; biorthogonal; vanishing viscosity; null-controllability; biorthogonal system},

language = {eng},

month = {2},

number = {1},

pages = {277-293},

publisher = {EDP Sciences},

title = {Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity},

url = {http://eudml.org/doc/276372},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Micu, Sorin

AU - Rovenţa, Ionel

TI - Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/2//

PB - EDP Sciences

VL - 18

IS - 1

SP - 277

EP - 293

AB - This article considers the linear 1-d Schrödinger equation in (0,π)
perturbed by a vanishing viscosity term depending on a small parameter
ε > 0. We study the boundary controllability properties of this
perturbed equation and the behavior of its boundary controls
vε as ε goes to zero. It
is shown that, for any time T sufficiently large but independent of
ε and for each initial datum in
H−1(0,π), there exists a uniformly bounded
family of controls
(vε)ε in
L2(0, T) acting on the extremity
x = π. Any weak limit of this family is a control for
the Schrödinger equation.

LA - eng

KW - Null-controllability; Schrödinger equation; complex Ginzburg-Landau equation; moment problem; biorthogonal; vanishing viscosity; null-controllability; biorthogonal system

UR - http://eudml.org/doc/276372

ER -

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