Downloads provided by UsageCountsExponential decay in one‐dimensional Type II/III thermoelasticity with two porosities
Copyright policy ) Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón;
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 introduce in the system a couple of dissipation mechanisms in order to obtain the exponential decay 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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thermal dissipation, :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], 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, double void, Viscoelasticitat, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Long-time behavior of solutions for dynamical problems in solid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Exponential decay., Exponential decay, Type II/III thermoelasticity with double voids, Thermoelasticity, :35 Partial differential equations::35Q Equations of mathematical physics and other areas of application [Classificació AMS], Viscosity, Viscoelasticity, Thermal effects in solid mechanics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Viscoporosity, viscoporosity, PDEs in connection with mechanics of deformable solids, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application, Termoelasticitat
thermal dissipation, :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], 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, double void, Viscoelasticitat, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Long-time behavior of solutions for dynamical problems in solid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Exponential decay., Exponential decay, Type II/III thermoelasticity with double voids, Thermoelasticity, :35 Partial differential equations::35Q Equations of mathematical physics and other areas of application [Classificació AMS], Viscosity, Viscoelasticity, Thermal effects in solid mechanics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Viscoporosity, viscoporosity, PDEs in connection with mechanics of deformable solids, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application, Termoelasticitat
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