Controllability of Schrödinger equation with a nonlocal term

Autores
de Leo, Mariano Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; Rial, Diego Fernando
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin, and for distributed controls supported outside of a fixed compact interval, the model equation is controllable. Moreover, it is shown that, for distributed controls with compact support, the exact controllability problem is not possible.
Fil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Nonlinear SchrödingerPoisson
Hartree potential
Constant electric field
Internal controllability.
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/30831
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/30831
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Controllability of Schrödinger equation with a nonlocal termde Leo, Mariano FernandoSanchez Fernandez de la Vega, Constanza MarielRial, Diego FernandoNonlinear SchrödingerPoissonHartree potentialConstant electric fieldInternal controllability.https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin, and for distributed controls supported outside of a fixed compact interval, the model equation is controllable. Moreover, it is shown that, for distributed controls with compact support, the exact controllability problem is not possible.Fil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sanchez Fernandez de la Vega, Constanza Mariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaEDP Sciences2013-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/30831Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; de Leo, Mariano Fernando; Controllability of Schrödinger equation with a nonlocal term; EDP Sciences; ESAIM-Control Optimisation and Calculus of Variations; 20; 1; 8-2013; 23-411262-3377CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/cocv/2013052info:eu-repo/semantics/altIdentifier/url/https://www.esaim-cocv.org/articles/cocv/abs/2014/01/cocv130052/cocv130052.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:11:03Zoai:ri.conicet.gov.ar:11336/30831instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:11:03.489CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Controllability of Schrödinger equation with a nonlocal term
title Controllability of Schrödinger equation with a nonlocal term
spellingShingle Controllability of Schrödinger equation with a nonlocal term
de Leo, Mariano Fernando
Nonlinear SchrödingerPoisson
Hartree potential
Constant electric field
Internal controllability.
title_short Controllability of Schrödinger equation with a nonlocal term
title_full Controllability of Schrödinger equation with a nonlocal term
title_fullStr Controllability of Schrödinger equation with a nonlocal term
title_full_unstemmed Controllability of Schrödinger equation with a nonlocal term
title_sort Controllability of Schrödinger equation with a nonlocal term
dc.creator.none.fl_str_mv de Leo, Mariano Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
Rial, Diego Fernando
author de Leo, Mariano Fernando
author_facet de Leo, Mariano Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
Rial, Diego Fernando
author_role author
author2 Sanchez Fernandez de la Vega, Constanza Mariel
Rial, Diego Fernando
author2_role author
author
dc.subject.none.fl_str_mv Nonlinear SchrödingerPoisson
Hartree potential
Constant electric field
Internal controllability.
topic Nonlinear SchrödingerPoisson
Hartree potential
Constant electric field
Internal controllability.
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin, and for distributed controls supported outside of a fixed compact interval, the model equation is controllable. Moreover, it is shown that, for distributed controls with compact support, the exact controllability problem is not possible.
Fil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin, and for distributed controls supported outside of a fixed compact interval, the model equation is controllable. Moreover, it is shown that, for distributed controls with compact support, the exact controllability problem is not possible.
publishDate 2013
dc.date.none.fl_str_mv 2013-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/30831
Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; de Leo, Mariano Fernando; Controllability of Schrödinger equation with a nonlocal term; EDP Sciences; ESAIM-Control Optimisation and Calculus of Variations; 20; 1; 8-2013; 23-41
1262-3377
CONICET Digital
CONICET
url http://hdl.handle.net/11336/30831
identifier_str_mv Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; de Leo, Mariano Fernando; Controllability of Schrödinger equation with a nonlocal term; EDP Sciences; ESAIM-Control Optimisation and Calculus of Variations; 20; 1; 8-2013; 23-41
1262-3377
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/cocv/2013052
info:eu-repo/semantics/altIdentifier/url/https://www.esaim-cocv.org/articles/cocv/abs/2014/01/cocv130052/cocv130052.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842270143029182464
score 13.13397

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