On the analyticity of the MGT-viscoelastic plate with heat conduction
We consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:2117/192903 |
| Acceso en línea: | https://hdl.handle.net/2117/192903 https://dx.doi.org/10.1016/j.jde.2020.05.043 |
| Access Level: | acceso abierto |
| Palabra clave: | Viscoelasticity Heat -- Conduction MGT equation Fourier heat conduction Type III heat conduction Analytic semigroups Viscoelasticitat Calor -- Conducció Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::74 Mechanics of deformable solids::74K Thin bodies, structures Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | We consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable Hilbert space. Then we prove that these semigroups are analytic, despite the fact that the semigroup generated by the mechanical equation alone does not share the same property. This means that the coupling with the heat equation produces a regularizing effect on the dynamics, implying in particular the impossibility of the localization of solutions. As a byproduct of our main result, the exponential stability of the semigroups is established. |
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