On the double Moore–Gibson–Thompson system of thermoviscoelasticity

In this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations (···u + aü - ß·u_xx - ¿u_xx = p(a·w_x + ¨w_x)) i (···w + ^a¨w - ^ß·w_xx - ^¿w_xx = ^p( ^a·u_xx + ü_x)) arising in the description of thermoviscoelastic materials. Here, a, ß, ¿, ^a, ^ß, ^¿ > 0...

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Autores: Dell'Oro, Filippo, Liverani, Lorenzo, Pata, Vittorino, Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/422886
Acceso en línea:https://hdl.handle.net/2117/422886
https://dx.doi.org/10.1111/sapm.12784
Access Level:acceso abierto
Palabra clave:Exponential stability
Moore–Gibson–Thompson system
Solution semigroup
Thermoviscoelasticity
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
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spelling On the double Moore–Gibson–Thompson system of thermoviscoelasticityDell'Oro, FilippoLiverani, LorenzoPata, VittorinoQuintanilla de Latorre, Ramón|||0000-0001-7059-7058Exponential stabilityMoore–Gibson–Thompson systemSolution semigroupThermoviscoelasticityÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciènciesIn this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations (···u + aü - ß·u_xx - ¿u_xx = p(a·w_x + ¨w_x)) i (···w + ^a¨w - ^ß·w_xx - ^¿w_xx = ^p( ^a·u_xx + ü_x)) arising in the description of thermoviscoelastic materials. Here, a, ß, ¿, ^a, ^ß, ^¿ > 0 while p^p > 0. When both the MGT equations lie in the subcritical regime, that is, ß - ¿/a > 0 and ^ß - ^¿/^a > 0 we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when a and ^a are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest."L.L. has been supported by the Alexander von Humboldt Foundation. F.D. and V.P. have been partially supported by the Italian MIUR-PRIN Grant 2020F3NCPX “Mathematics for industry 4.0 (Math4I4)”."Peer Reviewed20252025-01-0120252025-01-27journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/422886https://dx.doi.org/10.1111/sapm.12784reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4228862026-05-27T15:37:01Z
dc.title.none.fl_str_mv On the double Moore–Gibson–Thompson system of thermoviscoelasticity
title On the double Moore–Gibson–Thompson system of thermoviscoelasticity
spellingShingle On the double Moore–Gibson–Thompson system of thermoviscoelasticity
Dell'Oro, Filippo
Exponential stability
Moore–Gibson–Thompson system
Solution semigroup
Thermoviscoelasticity
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
title_short On the double Moore–Gibson–Thompson system of thermoviscoelasticity
title_full On the double Moore–Gibson–Thompson system of thermoviscoelasticity
title_fullStr On the double Moore–Gibson–Thompson system of thermoviscoelasticity
title_full_unstemmed On the double Moore–Gibson–Thompson system of thermoviscoelasticity
title_sort On the double Moore–Gibson–Thompson system of thermoviscoelasticity
dc.creator.none.fl_str_mv Dell'Oro, Filippo
Liverani, Lorenzo
Pata, Vittorino
Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
author Dell'Oro, Filippo
author_facet Dell'Oro, Filippo
Liverani, Lorenzo
Pata, Vittorino
Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
author_role author
author2 Liverani, Lorenzo
Pata, Vittorino
Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
author2_role author
author
author
dc.subject.none.fl_str_mv Exponential stability
Moore–Gibson–Thompson system
Solution semigroup
Thermoviscoelasticity
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
topic Exponential stability
Moore–Gibson–Thompson system
Solution semigroup
Thermoviscoelasticity
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
description In this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations (···u + aü - ß·u_xx - ¿u_xx = p(a·w_x + ¨w_x)) i (···w + ^a¨w - ^ß·w_xx - ^¿w_xx = ^p( ^a·u_xx + ü_x)) arising in the description of thermoviscoelastic materials. Here, a, ß, ¿, ^a, ^ß, ^¿ > 0 while p^p > 0. When both the MGT equations lie in the subcritical regime, that is, ß - ¿/a > 0 and ^ß - ^¿/^a > 0 we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when a and ^a are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-01
2025
2025-01-27
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://hdl.handle.net/2117/422886
https://dx.doi.org/10.1111/sapm.12784
url https://hdl.handle.net/2117/422886
https://dx.doi.org/10.1111/sapm.12784
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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