Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations

The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients. This compact...

Descripción completa

Detalles Bibliográficos
Autores: Briane, Marc, Casado Díaz, Juan
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/46225
Acceso en línea:http://hdl.handle.net/11441/46225
https://doi.org/10.1007/s00205-012-0520-9
Access Level:acceso abierto
Palabra clave:Homogenization
Plate
Stokes equation
Div-curl lemma
id ES_e11a24bbd74eeadb69cfaf5f6f190f23
oai_identifier_str oai:idus.us.es:11441/46225
network_acronym_str ES
network_name_str España
repository_id_str
spelling Homogenization of stiff plates and two-dimensional high-viscosity Stokes equationsBriane, MarcCasado Díaz, JuanHomogenizationPlateStokes equationDiv-curl lemmaThe paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients. This compactness result is based on a div-curl lemma for fourthorder equations. On the other hand, using an intermediate stream function we deduce from the plates case a similar result for high-viscosity Stokes equations in dimension two, so that the nature of the Stokes equation is preserved in the homogenization process. Finally, we show that the L1-boundedness assumption cannot be relaxed. Indeed, in the case of the Stokes equation the concentration of one very rigid strip on a line induces the appearance of second gradient terms in the limit problem, which violates the compactness result obtained under the L1-boundedness condition.Ministerio de Economía y CompetitividadSpringerEcuaciones Diferenciales y Análisis NuméricoFQM309: Control y Homogeneización de Ecuaciones en Derivadas ParcialesMinisterio de Economía y Competitividad (MINECO). España2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/46225https://doi.org/10.1007/s00205-012-0520-9reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésArchive for Rational Mechanics and Analysis, 205 (3), 753-794.info:eu-repo/grantAgreement/MINECO/MTM2011-24457/http://download.springer.com/static/pdf/356/art%253A10.1007%252Fs00205-012-0520-9.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00205-012-0520-9&token2=exp=1475055790~acl=%2Fstatic%2Fpdf%2F356%2Fart%25253A10.1007%25252Fs00205-012-0520-9.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00205-012-0520-9*~hmac=a11ab599cbbbf3e0fa4c82b178430a9d180bfedf79668893c05e60db7d8a74abinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/462252026-06-17T12:51:07Z
dc.title.none.fl_str_mv Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
title Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
spellingShingle Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
Briane, Marc
Homogenization
Plate
Stokes equation
Div-curl lemma
title_short Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
title_full Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
title_fullStr Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
title_full_unstemmed Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
title_sort Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
dc.creator.none.fl_str_mv Briane, Marc
Casado Díaz, Juan
author Briane, Marc
author_facet Briane, Marc
Casado Díaz, Juan
author_role author
author2 Casado Díaz, Juan
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Homogenization
Plate
Stokes equation
Div-curl lemma
topic Homogenization
Plate
Stokes equation
Div-curl lemma
description The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients. This compactness result is based on a div-curl lemma for fourthorder equations. On the other hand, using an intermediate stream function we deduce from the plates case a similar result for high-viscosity Stokes equations in dimension two, so that the nature of the Stokes equation is preserved in the homogenization process. Finally, we show that the L1-boundedness assumption cannot be relaxed. Indeed, in the case of the Stokes equation the concentration of one very rigid strip on a line induces the appearance of second gradient terms in the limit problem, which violates the compactness result obtained under the L1-boundedness condition.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/11441/46225
https://doi.org/10.1007/s00205-012-0520-9
url http://hdl.handle.net/11441/46225
https://doi.org/10.1007/s00205-012-0520-9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Archive for Rational Mechanics and Analysis, 205 (3), 753-794.
info:eu-repo/grantAgreement/MINECO/MTM2011-24457/
http://download.springer.com/static/pdf/356/art%253A10.1007%252Fs00205-012-0520-9.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00205-012-0520-9&token2=exp=1475055790~acl=%2Fstatic%2Fpdf%2F356%2Fart%25253A10.1007%25252Fs00205-012-0520-9.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00205-012-0520-9*~hmac=a11ab599cbbbf3e0fa4c82b178430a9d180bfedf79668893c05e60db7d8a74ab
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869422262560489472
score 15,300719

Similares en LA Referencia