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...
| Autores: | , |
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| 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 |
| 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. |
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