Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case

The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schrodinger equations, mainly the compactness of the support and its spatial localization. This question touches the very foundations underlying the derivation of the Schrodinger equation, since i...

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Detalhes bibliográficos
Autores: Díaz Díaz, Jesús Ildefonso, Begout, Pascal
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/42139
Acesso em linha:https://hdl.handle.net/20.500.14352/42139
Access Level:acceso abierto
Palavra-chave:517.928
singular complex potentials
operators
Nonlinear Schrodinger equation
Compact support
Energy method
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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network_acronym_str ES
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repository_id_str
spelling Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary caseDíaz Díaz, Jesús IldefonsoBegout, Pascal517.928singular complex potentialsoperatorsNonlinear Schrodinger equationCompact supportEnergy methodEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasThe main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schrodinger equations, mainly the compactness of the support and its spatial localization. This question touches the very foundations underlying the derivation of the Schrodinger equation, since it is well-known a solution of a linear Schrodinger equation perturbed by a regular potential never vanishes on a set of positive measure. A fact, which reflects the impossibility of locating the particle. Here we shall prove that if the perturbation involves suitable singular nonlinear terms then the support of the solution is a compact set, and so any estimate on its spatial localization implies very rich information on places not accessible by the particle. Our results are obtained by the application of certain energy methods which connect the compactness of the support with the local vanishing of a suitable "energy function" which satisfies a nonlinear differential inequality with an exponent less than one. The results improve and extend a previous short presentation by the authors published in 2006.Elsevier (Gauthier-Villars),Universidad Complutense de Madrid20122012-01-0120122012-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/42139reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/421392026-06-02T12:44:21Z
dc.title.none.fl_str_mv Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
title Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
spellingShingle Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
Díaz Díaz, Jesús Ildefonso
517.928
singular complex potentials
operators
Nonlinear Schrodinger equation
Compact support
Energy method
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
title_full Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
title_fullStr Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
title_full_unstemmed Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
title_sort Localizing estimates of the support of solutions of some nonlinear Schrodinger equations - The stationary case
dc.creator.none.fl_str_mv Díaz Díaz, Jesús Ildefonso
Begout, Pascal
author Díaz Díaz, Jesús Ildefonso
author_facet Díaz Díaz, Jesús Ildefonso
Begout, Pascal
author_role author
author2 Begout, Pascal
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.928
singular complex potentials
operators
Nonlinear Schrodinger equation
Compact support
Energy method
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.928
singular complex potentials
operators
Nonlinear Schrodinger equation
Compact support
Energy method
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schrodinger equations, mainly the compactness of the support and its spatial localization. This question touches the very foundations underlying the derivation of the Schrodinger equation, since it is well-known a solution of a linear Schrodinger equation perturbed by a regular potential never vanishes on a set of positive measure. A fact, which reflects the impossibility of locating the particle. Here we shall prove that if the perturbation involves suitable singular nonlinear terms then the support of the solution is a compact set, and so any estimate on its spatial localization implies very rich information on places not accessible by the particle. Our results are obtained by the application of certain energy methods which connect the compactness of the support with the local vanishing of a suitable "energy function" which satisfies a nonlinear differential inequality with an exponent less than one. The results improve and extend a previous short presentation by the authors published in 2006.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
2012
2012-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/42139
url https://hdl.handle.net/20.500.14352/42139
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier (Gauthier-Villars),
publisher.none.fl_str_mv Elsevier (Gauthier-Villars),
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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