Articles de revista
http://hdl.handle.net/2117/3339
Fri, 22 Mar 2019 14:07:13 GMT2019-03-22T14:07:13ZExponential decay in one-dimensional type III thermoelasticity with voids
http://hdl.handle.net/2117/130728
Exponential decay in one-dimensional type III thermoelasticity with voids
Miranville, Alain; Quintanilla de Latorre, Ramón
In this paper we consider the one-dimensional type III thermoelastic theory with voids. We prove that generically we have exponential stability of the solutions. This is a striking fact if one compares it with the behavior in the case of the thermoelastic theory based on the classical Fourier law for which the decayis generically slower.
Thu, 21 Mar 2019 15:04:25 GMThttp://hdl.handle.net/2117/1307282019-03-21T15:04:25ZMiranville, AlainQuintanilla de Latorre, RamónIn this paper we consider the one-dimensional type III thermoelastic theory with voids. We prove that generically we have exponential stability of the solutions. This is a striking fact if one compares it with the behavior in the case of the thermoelastic theory based on the classical Fourier law for which the decayis generically slower.On quasi-static approximations in linear thermoelastodynamics
http://hdl.handle.net/2117/129128
On quasi-static approximations in linear thermoelastodynamics
Knops, Robin J.; Quintanilla de Latorre, Ramón
The validity of the coupled and uncoupled quasi-static approximations is considered for the initial boundary value problem of linear thermoelasticity subject to homoge-neous Dirichlet boundary conditions, and for solutions and their derivatives that are mean-square integrable. Essential components in the proof, of independent interest, are conservation laws and associated estimates for the exact and approximate systems
Thu, 14 Feb 2019 12:41:32 GMThttp://hdl.handle.net/2117/1291282019-02-14T12:41:32ZKnops, Robin J.Quintanilla de Latorre, RamónThe validity of the coupled and uncoupled quasi-static approximations is considered for the initial boundary value problem of linear thermoelasticity subject to homoge-neous Dirichlet boundary conditions, and for solutions and their derivatives that are mean-square integrable. Essential components in the proof, of independent interest, are conservation laws and associated estimates for the exact and approximate systemsNumerical analysis of a thermoelastic problem with dual-phase-lag heat conduction
http://hdl.handle.net/2117/129114
Numerical analysis of a thermoelastic problem with dual-phase-lag heat conduction
Bazarra, Noelia; Campo, Marco; Fernández, José Ramón; Quintanilla de Latorre, Ramón
In this paper we study, from the numerical point of view, a thermoelastic problem with dual-phase-lag heat conduction. The variational formulation is written as a coupled system of hyperbolic linear variational equations. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A discrete stability result is proved and a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.
Thu, 14 Feb 2019 11:31:05 GMThttp://hdl.handle.net/2117/1291142019-02-14T11:31:05ZBazarra, NoeliaCampo, MarcoFernández, José RamónQuintanilla de Latorre, RamónIn this paper we study, from the numerical point of view, a thermoelastic problem with dual-phase-lag heat conduction. The variational formulation is written as a coupled system of hyperbolic linear variational equations. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A discrete stability result is proved and a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.Numerical resolution of an exact heat conduction model with a delay term
http://hdl.handle.net/2117/128337
Numerical resolution of an exact heat conduction model with a delay term
Campo, Marco; Fernández, José Ramón; Quintanilla de Latorre, Ramón
In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.
Mon, 04 Feb 2019 14:52:58 GMThttp://hdl.handle.net/2117/1283372019-02-04T14:52:58ZCampo, MarcoFernández, José RamónQuintanilla de Latorre, RamónIn this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.Viscoelastic materials with a double porosity structure
http://hdl.handle.net/2117/127597
Viscoelastic materials with a double porosity structure
Iesan, Dorin; Quintanilla de Latorre, Ramón
This paper in concerned with the linear theory of materials with memory that possess a double porosity structure. First, the formulation of the initial-boundary-value problem is presented. Then, a uniqueness result is established. The semigroup theory of linear operators is used to prove existence and continuous dependence of solutions. A minimum principle for the dynamical theory is also derived.
Fri, 25 Jan 2019 12:38:15 GMThttp://hdl.handle.net/2117/1275972019-01-25T12:38:15ZIesan, DorinQuintanilla de Latorre, RamónThis paper in concerned with the linear theory of materials with memory that possess a double porosity structure. First, the formulation of the initial-boundary-value problem is presented. Then, a uniqueness result is established. The semigroup theory of linear operators is used to prove existence and continuous dependence of solutions. A minimum principle for the dynamical theory is also derived.Qualitative results for a mixture of Green-Lindsay thermoelastic solids
http://hdl.handle.net/2117/125861
Qualitative results for a mixture of Green-Lindsay thermoelastic solids
Magaña Nieto, Antonio; Muñoz Rivera, Jaime E.; Naso, Maria Grazia; Quintanilla de Latorre, Ramón
We study qualitative properties of the solutions of the system of partial
differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity e ects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of
the solutions over the time. We use the semigroup arguments to establish our results
Mon, 17 Dec 2018 12:35:05 GMThttp://hdl.handle.net/2117/1258612018-12-17T12:35:05ZMagaña Nieto, AntonioMuñoz Rivera, Jaime E.Naso, Maria GraziaQuintanilla de Latorre, RamónWe study qualitative properties of the solutions of the system of partial
differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity e ects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of
the solutions over the time. We use the semigroup arguments to establish our resultsNumerical analysis of some dual-phase-lag models
http://hdl.handle.net/2117/122914
Numerical analysis of some dual-phase-lag models
Bazarra, Noelia; Copetti, Maria; Fernández, José Ramón; Quintanilla de Latorre, Ramón
In this paper we analyse, from the numerical point of view, two dual-phase-lag models appearing in the heat conduction theory. Both models are written as linear partial differential equations of third order in time. The variational formulations, written in terms of the thermal acceleration, lead to linear variational equations, for which existence and uniqueness
results, and energy decay properties, are recalled. Then, fully discrete approximations are introduced for both models using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Discrete stability properties are proved, and a priori error estimates are obtained, from which the linear convergence of the approximations is derived. Finally, some numerical simulations are described in one and two dimensions to demonstrate the accuracy of the approximations and the behaviour of the solutions
Wed, 24 Oct 2018 10:52:27 GMThttp://hdl.handle.net/2117/1229142018-10-24T10:52:27ZBazarra, NoeliaCopetti, MariaFernández, José RamónQuintanilla de Latorre, RamónIn this paper we analyse, from the numerical point of view, two dual-phase-lag models appearing in the heat conduction theory. Both models are written as linear partial differential equations of third order in time. The variational formulations, written in terms of the thermal acceleration, lead to linear variational equations, for which existence and uniqueness
results, and energy decay properties, are recalled. Then, fully discrete approximations are introduced for both models using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Discrete stability properties are proved, and a priori error estimates are obtained, from which the linear convergence of the approximations is derived. Finally, some numerical simulations are described in one and two dimensions to demonstrate the accuracy of the approximations and the behaviour of the solutionsExponential stability in type III thermoelasticity with microtemperatures
http://hdl.handle.net/2117/122813
Exponential stability in type III thermoelasticity with microtemperatures
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this paper we consider the type III thermoelastic theory with microtemperatures. We study the time decay of the solutions and we prove that under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow shocking because it differs from the behavior of the solutions in the classical model of thermoelasticity with microtemperatures
Tue, 23 Oct 2018 11:33:17 GMThttp://hdl.handle.net/2117/1228132018-10-23T11:33:17ZMagaña Nieto, AntonioQuintanilla de Latorre, RamónIn this paper we consider the type III thermoelastic theory with microtemperatures. We study the time decay of the solutions and we prove that under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow shocking because it differs from the behavior of the solutions in the classical model of thermoelasticity with microtemperaturesSome qualitative results for a modification of the Green–Lindsay thermoelasticity
http://hdl.handle.net/2117/122738
Some qualitative results for a modification of the Green–Lindsay thermoelasticity
Quintanilla de Latorre, Ramón
In this short note we consider a recent modification of the Green–Lindsay thermoelastic theory proposed at Yu et al. (Meccanica 53:2543–2554, 2018). We consider a functional defined on the solutions of the problem. It allows us to obtain the continuous dependence of the solutions with respect to the initial conditions and to the supply terms, the time exponential decay of solutions and an alternative of Phragme´n–Lindelo¨f type for the spatial behaviour.
Mon, 22 Oct 2018 12:37:57 GMThttp://hdl.handle.net/2117/1227382018-10-22T12:37:57ZQuintanilla de Latorre, RamónIn this short note we consider a recent modification of the Green–Lindsay thermoelastic theory proposed at Yu et al. (Meccanica 53:2543–2554, 2018). We consider a functional defined on the solutions of the problem. It allows us to obtain the continuous dependence of the solutions with respect to the initial conditions and to the supply terms, the time exponential decay of solutions and an alternative of Phragme´n–Lindelo¨f type for the spatial behaviour.Decay rates of Saint-Venant type for a functionally graded heat-conducting hollowed cylinder
http://hdl.handle.net/2117/122731
Decay rates of Saint-Venant type for a functionally graded heat-conducting hollowed cylinder
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this paper we consider the case of a functionally graded heat-conducting hollowed cylinder. Our purpose is to investigate the consequences of the material inhomogeneity on the decay of Saint-Venant end effects in the case of linear isotropic rigid solids. The mathematical issues involve the implications of spatial inhomogeneity on the decay rates of solutions to Dirichlet boundary-value problems. The rate of decay is characterized in terms of the smallest eigenvalue of a Sturm–Liouville problem. We first consider the case where the inhomogeneity depends on the radius of the cross-section, but later we also consider the case where the inhomogeneity also depends on the axial variable. The last section
considers the case where the cross-section is increasing. Some tables and figures illustrate our estimates.
Mon, 22 Oct 2018 11:34:25 GMThttp://hdl.handle.net/2117/1227312018-10-22T11:34:25ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn this paper we consider the case of a functionally graded heat-conducting hollowed cylinder. Our purpose is to investigate the consequences of the material inhomogeneity on the decay of Saint-Venant end effects in the case of linear isotropic rigid solids. The mathematical issues involve the implications of spatial inhomogeneity on the decay rates of solutions to Dirichlet boundary-value problems. The rate of decay is characterized in terms of the smallest eigenvalue of a Sturm–Liouville problem. We first consider the case where the inhomogeneity depends on the radius of the cross-section, but later we also consider the case where the inhomogeneity also depends on the axial variable. The last section
considers the case where the cross-section is increasing. Some tables and figures illustrate our estimates.