Dispersion for 1-d Schrödinger and wave equations with bv coefficients

In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough b...

Descripción completa

Detalles Bibliográficos
Autores: Beli, N., Ignat, L.I., Zuazua, E.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2016
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/265
Acceso en línea:http://hdl.handle.net/20.500.11824/265
Access Level:acceso abierto
Palabra clave:Schrödinger equation
Wave equation
One space dimension
BV coefficients
Dispersion and Strichartz estimates
Almost periodic functions
id ES_47633aebd43243cb7f5fd9ba8f2beb06
oai_identifier_str oai:bird.bcamath.org:20.500.11824/265
network_acronym_str ES
network_name_str España
repository_id_str
spelling Dispersion for 1-d Schrödinger and wave equations with bv coefficientsBeli, N.Ignat, L.I.Zuazua, E.Schrödinger equationWave equationOne space dimensionBV coefficientsDispersion and Strichartz estimatesAlmost periodic functionsIn this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrödinger equation we prove that the dispersion holds under the same smallness assumption on the variation of the coefficient. But, whether dispersion may fail for larger coefficients is unknown for the Schrödinger equation.201620162016info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/265reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttp://www.sciencedirect.com/science/article/pii/S029414491500061Xinfo:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01info:eu-repo/grantAgreement/EC/FP7/246775Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/2652026-06-19T12:47:47Z
dc.title.none.fl_str_mv Dispersion for 1-d Schrödinger and wave equations with bv coefficients
title Dispersion for 1-d Schrödinger and wave equations with bv coefficients
spellingShingle Dispersion for 1-d Schrödinger and wave equations with bv coefficients
Beli, N.
Schrödinger equation
Wave equation
One space dimension
BV coefficients
Dispersion and Strichartz estimates
Almost periodic functions
title_short Dispersion for 1-d Schrödinger and wave equations with bv coefficients
title_full Dispersion for 1-d Schrödinger and wave equations with bv coefficients
title_fullStr Dispersion for 1-d Schrödinger and wave equations with bv coefficients
title_full_unstemmed Dispersion for 1-d Schrödinger and wave equations with bv coefficients
title_sort Dispersion for 1-d Schrödinger and wave equations with bv coefficients
dc.creator.none.fl_str_mv Beli, N.
Ignat, L.I.
Zuazua, E.
author Beli, N.
author_facet Beli, N.
Ignat, L.I.
Zuazua, E.
author_role author
author2 Ignat, L.I.
Zuazua, E.
author2_role author
author
dc.subject.none.fl_str_mv Schrödinger equation
Wave equation
One space dimension
BV coefficients
Dispersion and Strichartz estimates
Almost periodic functions
topic Schrödinger equation
Wave equation
One space dimension
BV coefficients
Dispersion and Strichartz estimates
Almost periodic functions
description In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrödinger equation we prove that the dispersion holds under the same smallness assumption on the variation of the coefficient. But, whether dispersion may fail for larger coefficients is unknown for the Schrödinger equation.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/265
url http://hdl.handle.net/20.500.11824/265
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://www.sciencedirect.com/science/article/pii/S029414491500061X
info:eu-repo/grantAgreement/MICINN//MTM2011-29306-C02-01
info:eu-repo/grantAgreement/EC/FP7/246775
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407291336294400
score 15.301603

Similares en LA Referencia