Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity

This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr¨odinger equation when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F(|u|2)u = a "+(|u|2)α u, with a 2 C, " > 0, 2 = (1 − m) and m...

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Detalles Bibliográficos
Autores: Díaz Díaz, Jesús Ildefonso, Begout, Pascal
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/72649
Acceso en línea:https://hdl.handle.net/20.500.14352/72649
Access Level:acceso abierto
Palabra clave:517
517.9
Partial differential equations
Stability in context of PDEs
NLS equations
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
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oai_identifier_str oai:docta.ucm.es:20.500.14352/72649
network_acronym_str ES
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repository_id_str
spelling Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearityDíaz Díaz, Jesús IldefonsoBegout, Pascal517517.9Partial differential equationsStability in context of PDEsNLS equationsAnálisis matemáticoEcuaciones diferenciales1202 Análisis y Análisis Funcional1202.07 Ecuaciones en DiferenciasThis paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr¨odinger equation when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F(|u|2)u = a "+(|u|2)α u, with a 2 C, " > 0, 2 = (1 − m) and m 2 [0, 1). Here we consider the sublinear case 0 < m < 1 with a critical damped coefficient: a 2 C is assumed to be in the set D(m) = z 2 C; Im(z) > 0 and 2pmIm(z) = (1−m)Re(z). Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel′muter [16] and the more recent study by Cialdea and Maz′ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains.KhayyamUniversidad Complutense de Madrid20232023-01-0120232023-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/72649reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/726492026-06-02T12:44:21Z
dc.title.none.fl_str_mv Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
title Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
spellingShingle Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
Díaz Díaz, Jesús Ildefonso
517
517.9
Partial differential equations
Stability in context of PDEs
NLS equations
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
title_short Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
title_full Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
title_fullStr Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
title_full_unstemmed Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
title_sort Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
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
517.9
Partial differential equations
Stability in context of PDEs
NLS equations
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
topic 517
517.9
Partial differential equations
Stability in context of PDEs
NLS equations
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
description This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr¨odinger equation when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F(|u|2)u = a "+(|u|2)α u, with a 2 C, " > 0, 2 = (1 − m) and m 2 [0, 1). Here we consider the sublinear case 0 < m < 1 with a critical damped coefficient: a 2 C is assumed to be in the set D(m) = z 2 C; Im(z) > 0 and 2pmIm(z) = (1−m)Re(z). Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel′muter [16] and the more recent study by Cialdea and Maz′ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01
2023
2023-01-01
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/20.500.14352/72649
url https://hdl.handle.net/20.500.14352/72649
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 Khayyam
publisher.none.fl_str_mv Khayyam
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 15,301603

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