Non-Homogeneous Thermoelastic Timoshenko Systems
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | LOCUS Repositório Institucional da UFV |
Texto Completo: | https://doi.org/10.1007/s00574-017-0030-3 http://www.locus.ufv.br/handle/123456789/22045 |
Resumo: | The well-established Timoshenko system is characterized by a particular relation between shear stress and bending moment from its constitutive equations. Accordingly, a (thermal) dissipation added on the bending moment produces exponential stability if and only if the so called “equal wave speeds” condition is satisfied. This remarkable property extends to the case of non-homogeneous coefficients. In this paper, we consider a non-homogeneous thermoelastic system with dissipation restricted to the shear stress. To this new problem, by means of a delicate control observability analysis, we prove that a local version of the equal wave speeds condition is sufficient for the exponential stability of the system. Otherwise, we study the polynomial stability of the system with decay rate depending on the regularity of initial data. |
id |
UFV_50c41d0345205f18f9e0e2589c345b12 |
---|---|
oai_identifier_str |
oai:locus.ufv.br:123456789/22045 |
network_acronym_str |
UFV |
network_name_str |
LOCUS Repositório Institucional da UFV |
repository_id_str |
2145 |
spelling |
Alves, M. S.Silva, M. A. JorgeMa, T. F.Rivera, J. E. Muñoz2018-09-27T01:10:48Z2018-09-27T01:10:48Z2017-091678-7714https://doi.org/10.1007/s00574-017-0030-3http://www.locus.ufv.br/handle/123456789/22045The well-established Timoshenko system is characterized by a particular relation between shear stress and bending moment from its constitutive equations. Accordingly, a (thermal) dissipation added on the bending moment produces exponential stability if and only if the so called “equal wave speeds” condition is satisfied. This remarkable property extends to the case of non-homogeneous coefficients. In this paper, we consider a non-homogeneous thermoelastic system with dissipation restricted to the shear stress. To this new problem, by means of a delicate control observability analysis, we prove that a local version of the equal wave speeds condition is sufficient for the exponential stability of the system. Otherwise, we study the polynomial stability of the system with decay rate depending on the regularity of initial data.engBulletin of the Brazilian Mathematical Society, New SeriesVolume 48, Issue 3, p. 461–484, September 2017Springer Berlin Heidelberginfo:eu-repo/semantics/openAccessTimoshenko systemsThermoelasticityNon-homogeneous coefficientsExponential stabilityPolynomial stabilityNon-Homogeneous Thermoelastic Timoshenko Systemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdfTexto completoapplication/pdf630732https://locus.ufv.br//bitstream/123456789/22045/1/artigo.pdfbcc437b068a332f3427c7c92c80971d8MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/22045/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg4563https://locus.ufv.br//bitstream/123456789/22045/3/artigo.pdf.jpg7814c600e3b4664480feebc0989a45a0MD53123456789/220452018-09-26 23:00:56.339oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-09-27T02:00:56LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false |
dc.title.en.fl_str_mv |
Non-Homogeneous Thermoelastic Timoshenko Systems |
title |
Non-Homogeneous Thermoelastic Timoshenko Systems |
spellingShingle |
Non-Homogeneous Thermoelastic Timoshenko Systems Alves, M. S. Timoshenko systems Thermoelasticity Non-homogeneous coefficients Exponential stability Polynomial stability |
title_short |
Non-Homogeneous Thermoelastic Timoshenko Systems |
title_full |
Non-Homogeneous Thermoelastic Timoshenko Systems |
title_fullStr |
Non-Homogeneous Thermoelastic Timoshenko Systems |
title_full_unstemmed |
Non-Homogeneous Thermoelastic Timoshenko Systems |
title_sort |
Non-Homogeneous Thermoelastic Timoshenko Systems |
author |
Alves, M. S. |
author_facet |
Alves, M. S. Silva, M. A. Jorge Ma, T. F. Rivera, J. E. Muñoz |
author_role |
author |
author2 |
Silva, M. A. Jorge Ma, T. F. Rivera, J. E. Muñoz |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Alves, M. S. Silva, M. A. Jorge Ma, T. F. Rivera, J. E. Muñoz |
dc.subject.pt-BR.fl_str_mv |
Timoshenko systems Thermoelasticity Non-homogeneous coefficients Exponential stability Polynomial stability |
topic |
Timoshenko systems Thermoelasticity Non-homogeneous coefficients Exponential stability Polynomial stability |
description |
The well-established Timoshenko system is characterized by a particular relation between shear stress and bending moment from its constitutive equations. Accordingly, a (thermal) dissipation added on the bending moment produces exponential stability if and only if the so called “equal wave speeds” condition is satisfied. This remarkable property extends to the case of non-homogeneous coefficients. In this paper, we consider a non-homogeneous thermoelastic system with dissipation restricted to the shear stress. To this new problem, by means of a delicate control observability analysis, we prove that a local version of the equal wave speeds condition is sufficient for the exponential stability of the system. Otherwise, we study the polynomial stability of the system with decay rate depending on the regularity of initial data. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-09 |
dc.date.accessioned.fl_str_mv |
2018-09-27T01:10:48Z |
dc.date.available.fl_str_mv |
2018-09-27T01:10:48Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.1007/s00574-017-0030-3 http://www.locus.ufv.br/handle/123456789/22045 |
dc.identifier.issn.none.fl_str_mv |
1678-7714 |
identifier_str_mv |
1678-7714 |
url |
https://doi.org/10.1007/s00574-017-0030-3 http://www.locus.ufv.br/handle/123456789/22045 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.pt-BR.fl_str_mv |
Volume 48, Issue 3, p. 461–484, September 2017 |
dc.rights.driver.fl_str_mv |
Springer Berlin Heidelberg info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Springer Berlin Heidelberg |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Bulletin of the Brazilian Mathematical Society, New Series |
publisher.none.fl_str_mv |
Bulletin of the Brazilian Mathematical Society, New Series |
dc.source.none.fl_str_mv |
reponame:LOCUS Repositório Institucional da UFV instname:Universidade Federal de Viçosa (UFV) instacron:UFV |
instname_str |
Universidade Federal de Viçosa (UFV) |
instacron_str |
UFV |
institution |
UFV |
reponame_str |
LOCUS Repositório Institucional da UFV |
collection |
LOCUS Repositório Institucional da UFV |
bitstream.url.fl_str_mv |
https://locus.ufv.br//bitstream/123456789/22045/1/artigo.pdf https://locus.ufv.br//bitstream/123456789/22045/2/license.txt https://locus.ufv.br//bitstream/123456789/22045/3/artigo.pdf.jpg |
bitstream.checksum.fl_str_mv |
bcc437b068a332f3427c7c92c80971d8 8a4605be74aa9ea9d79846c1fba20a33 7814c600e3b4664480feebc0989a45a0 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 |
repository.name.fl_str_mv |
LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV) |
repository.mail.fl_str_mv |
fabiojreis@ufv.br |
_version_ |
1798053195316985856 |