Articles de revista
http://hdl.handle.net/2117/3339
2019-05-19T13:09:01ZSome remarks on the fast spatial growth/decay in exterior regions
http://hdl.handle.net/2117/132926
Some remarks on the fast spatial growth/decay in exterior regions
Quintanilla de Latorre, Ramón
In this paper we investigate the spatial behavior of the solutions to several partial differential equations/systems for exterior or cone-like regions. Under certain conditions for the equations we prove that the growth/decay estimates are faster than any exponential depending linearly on the distance to the origin. This kind of spatial behavior has not been noticed previously for parabolic problems and exterior or cone-like regions. The results obtained in this work apply in particular for the linear case.
2019-05-13T08:56:43ZQuintanilla de Latorre, RamónIn this paper we investigate the spatial behavior of the solutions to several partial differential equations/systems for exterior or cone-like regions. Under certain conditions for the equations we prove that the growth/decay estimates are faster than any exponential depending linearly on the distance to the origin. This kind of spatial behavior has not been noticed previously for parabolic problems and exterior or cone-like regions. The results obtained in this work apply in particular for the linear case.On the uniqueness and analyticity in viscoelasticity with double porosity
http://hdl.handle.net/2117/131999
On the uniqueness and analyticity in viscoelasticity with double porosity
Bazarra, Noelia; Fernández, José Ramón; Leseduarte Milán, María Carme; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained.
2019-04-25T10:14:26ZBazarra, NoeliaFernández, José RamónLeseduarte Milán, María CarmeMagaña Nieto, AntonioQuintanilla de Latorre, RamónIn this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained.Decay rates of Saint-Venant type for functionally graded heat-conducting materials
http://hdl.handle.net/2117/130813
Decay rates of Saint-Venant type for functionally graded heat-conducting materials
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
This paper investigates decay rates for the spatial behaviour of solutions for functionally graded heat-conducting materials. From a mathematical point of view, we obtain a new inequality of Poincarétype. This new result allows us to give new decay rates for functionally graded materials when the inhomogeneity depends on the radial variable and the axial variable of the cylinder. The case when the cross-section is increasing is also considered. Besides, we propose to obtain estimates for the case of mixtures. Some pictures illustrate our estimates.
2019-03-25T13:22:52ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónThis paper investigates decay rates for the spatial behaviour of solutions for functionally graded heat-conducting materials. From a mathematical point of view, we obtain a new inequality of Poincarétype. This new result allows us to give new decay rates for functionally graded materials when the inhomogeneity depends on the radial variable and the axial variable of the cylinder. The case when the cross-section is increasing is also considered. Besides, we propose to obtain estimates for the case of mixtures. Some pictures illustrate our estimates.Exponential 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.
2019-03-21T15:04:25ZMiranville, 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
2019-02-14T12:41:32ZKnops, 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.
2019-02-14T11:31:05ZBazarra, 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.
2019-02-04T14:52:58ZCampo, 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.
2019-01-25T12:38:15ZIesan, 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
2018-12-17T12:35:05ZMagaña 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
2018-10-24T10:52:27ZBazarra, 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 solutions