On a mixture of an MGT viscous material and an elastic solid

A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelasti...

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Detalles Bibliográficos
Autores: Fernández, Jose R., Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
Tipo de recurso: artículo
Fecha de publicación:2022
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:2117/361717
Acceso en línea:https://hdl.handle.net/2117/361717
https://dx.doi.org/10.1007/s00707-021-03124-z
Access Level:acceso abierto
Palabra clave:Thermoelasticity
Viscoelasticity
Mixture
Moore-Gibson-Thompson material
Existence and uniqueness
Exponential energy decay
Termoelasticitat
Viscoelasticitat
Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects
Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Descripción
Sumario:A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelastic type material and an elastic solid. To this end, we first derive the system of equations governing the deformations of such material. We give the suitable assumptions to obtain an existence and uniqueness result. The semigroups theory of linear operators is used. The paper concludes by proving the exponential decay of solutions with the help of a characterization of the exponentially stable semigroups of contractions and introducing an extra assumption. The impossibility of location is also shown.