Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation

[EN] We study a third-order partial differential equation in the form $\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$ that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures....

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Detalles Bibliográficos
Autores: Conejero, J. Alberto|||0000-0003-3681-7533, Ródenas Escribá, Francisco De Asís|||0000-0003-4564-5171, Lizama, Carlos
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/64842
Acceso en línea:https://riunet.upv.es/handle/10251/64842
Access Level:acceso abierto
Palabra clave:Acoustics
C0-semigroups
Devaney chaos
Hypercyclicity
Moore-Gibson-Thompson equation
Sound propagation
MATEMATICA APLICADA
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spelling Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equationConejero, J. Alberto|||0000-0003-3681-7533Ródenas Escribá, Francisco De Asís|||0000-0003-4564-5171Lizama, CarlosAcousticsC0-semigroupsDevaney chaosHypercyclicityMoore-Gibson-Thompson equationSound propagationMATEMATICA APLICADA[EN] We study a third-order partial differential equation in the form $\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$ that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter $\gamma:=\alpha-\frac{\tauc^2}{b}$ is negative, the equation (1) admits an uniformly continuous, chaotic and topologically mixing semigroup on Banach spaces of Herzog s type.The first and third authors are supported in part by MEC Project MTM2013-47093-P. The second author is partially supported by Project Anillo ACT1112. The authors are grateful to an anonymous referee for helpful comments that improved the presentation of the paper.Natural Sciences PublishingDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaComisión Nacional de Investigación Científica y Tecnológica, ChileMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-09-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/64842reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2013-47093-P HIPERCICLICIDAD Y CAOS DE OPERADORESComisión Nacional de Investigación Científica y Tecnológica, Chile https://doi.org/10.13039/501100009068 ACT1112open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/648422026-06-13T07:49:27Z
dc.title.none.fl_str_mv Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
title Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
spellingShingle Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
Conejero, J. Alberto|||0000-0003-3681-7533
Acoustics
C0-semigroups
Devaney chaos
Hypercyclicity
Moore-Gibson-Thompson equation
Sound propagation
MATEMATICA APLICADA
title_short Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
title_full Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
title_fullStr Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
title_full_unstemmed Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
title_sort Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
dc.creator.none.fl_str_mv Conejero, J. Alberto|||0000-0003-3681-7533
Ródenas Escribá, Francisco De Asís|||0000-0003-4564-5171
Lizama, Carlos
author Conejero, J. Alberto|||0000-0003-3681-7533
author_facet Conejero, J. Alberto|||0000-0003-3681-7533
Ródenas Escribá, Francisco De Asís|||0000-0003-4564-5171
Lizama, Carlos
author_role author
author2 Ródenas Escribá, Francisco De Asís|||0000-0003-4564-5171
Lizama, Carlos
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
Comisión Nacional de Investigación Científica y Tecnológica, Chile
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Acoustics
C0-semigroups
Devaney chaos
Hypercyclicity
Moore-Gibson-Thompson equation
Sound propagation
MATEMATICA APLICADA
topic Acoustics
C0-semigroups
Devaney chaos
Hypercyclicity
Moore-Gibson-Thompson equation
Sound propagation
MATEMATICA APLICADA
description [EN] We study a third-order partial differential equation in the form $\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$ that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter $\gamma:=\alpha-\frac{\tauc^2}{b}$ is negative, the equation (1) admits an uniformly continuous, chaotic and topologically mixing semigroup on Banach spaces of Herzog s type.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-09-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/64842
url https://riunet.upv.es/handle/10251/64842
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2013-47093-P HIPERCICLICIDAD Y CAOS DE OPERADORES
Comisión Nacional de Investigación Científica y Tecnológica, Chile https://doi.org/10.13039/501100009068 ACT1112
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Natural Sciences Publishing
publisher.none.fl_str_mv Natural Sciences Publishing
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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