Exponential decay in one-dimensional Type II/III thermoelasticity with two porosities
In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introdu...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/187178 |
| Acesso em linha: | https://hdl.handle.net/2117/187178 https://dx.doi.org/10.1002/mma.6438 |
| Access Level: | acceso abierto |
| Palavra-chave: | Thermoelasticity Viscoelasticity Type II/III thermoelasticity with double voids Viscosity Viscoporosity Exponential decay. Termoelasticitat Viscoelasticitat Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Resumo: | In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de- cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained. |
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