Articles de revista
http://hdl.handle.net/2117/3339
Sat, 24 Mar 2018 22:04:33 GMT2018-03-24T22:04:33ZSpatial behavior in high order partial differential equations
http://hdl.handle.net/2117/115596
Spatial behavior in high order partial differential equations
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this paper we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phase-lag theories, reflecting Saint-Venant's principle. In a recent paper, two families of cases for high order partial differential equations were studied. Here we investigate a third family of cases which corresponds to the fact that a certain condition on the time derivative must be satis ed. We also study the spatial behavior of a thermoelastic problem. We obtain a Phragmén-Lindelöf alternative for the solutions in both cases. The main tool to handle these problems is the use of an exponentially weighted Poincaré inequality.
Fri, 23 Mar 2018 09:31:04 GMThttp://hdl.handle.net/2117/1155962018-03-23T09:31:04ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn this paper we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phase-lag theories, reflecting Saint-Venant's principle. In a recent paper, two families of cases for high order partial differential equations were studied. Here we investigate a third family of cases which corresponds to the fact that a certain condition on the time derivative must be satis ed. We also study the spatial behavior of a thermoelastic problem. We obtain a Phragmén-Lindelöf alternative for the solutions in both cases. The main tool to handle these problems is the use of an exponentially weighted Poincaré inequality.Qualitative properties in strain gradient thermoelasticity with microtemperatures
http://hdl.handle.net/2117/114271
Qualitative properties in strain gradient thermoelasticity with microtemperatures
Iesan, Dorin; Quintanilla de Latorre, Ramón
This paper is devoted to the strain gradient theory of thermoelastic aterials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded body
Tue, 20 Feb 2018 09:23:05 GMThttp://hdl.handle.net/2117/1142712018-02-20T09:23:05ZIesan, DorinQuintanilla de Latorre, RamónThis paper is devoted to the strain gradient theory of thermoelastic aterials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded bodyOn the existence and uniqueness in phase-lag thermoelasticity
http://hdl.handle.net/2117/114238
On the existence and uniqueness in phase-lag thermoelasticity
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper is devoted to analyze the phaselag thermoelasticity problem. We study two different cases and we prove, for each one of them, that the
solutions of the problem are determined by a quasicontractive semigroup. As a consequence, existence, uniqueness and continuous dependence of the solutions are obtained
Mon, 19 Feb 2018 13:26:46 GMThttp://hdl.handle.net/2117/1142382018-02-19T13:26:46ZMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis paper is devoted to analyze the phaselag thermoelasticity problem. We study two different cases and we prove, for each one of them, that the
solutions of the problem are determined by a quasicontractive semigroup. As a consequence, existence, uniqueness and continuous dependence of the solutions are obtainedPhragmén-Lindelöf alternative for the Laplace equation with dynamic boundary conditions
http://hdl.handle.net/2117/109213
Phragmén-Lindelöf alternative for the Laplace equation with dynamic boundary conditions
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
This paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on its lateral side. We prove a Phragmén-Lindelöf
alternative for the solutions. To be precise, we see that the solutions
increase in an exponential way or they decay as a polynomial. To give a
complete description of the decay in this last case we also obtain an upper
bound for the amplitude term by means of the boundary conditions. In the
last section we sketch how to generalize the results to a system of two elliptic equations related with the heat conduction in mixtures.
Wed, 25 Oct 2017 15:40:59 GMThttp://hdl.handle.net/2117/1092132017-10-25T15:40:59ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónThis paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on its lateral side. We prove a Phragmén-Lindelöf
alternative for the solutions. To be precise, we see that the solutions
increase in an exponential way or they decay as a polynomial. To give a
complete description of the decay in this last case we also obtain an upper
bound for the amplitude term by means of the boundary conditions. In the
last section we sketch how to generalize the results to a system of two elliptic equations related with the heat conduction in mixtures.Time decay in dual-phase-lag thermoelasticity: critical case
http://hdl.handle.net/2117/108915
Time decay in dual-phase-lag thermoelasticity: critical case
Liu, Zhuangyi; Quintanilla de Latorre, Ramón
This note is devoted to the study of the time decay of the onedimensional dual-phase-lag thermoelasticity. In this theory two delay parameters tq and t¿ are proposed. It is known that the system is exponentially stable if tq < 2t¿ [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that tq = 2t¿ as well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper sub-interval of the spatial domain, when t¿ is spatially dependent.
Fri, 20 Oct 2017 11:43:29 GMThttp://hdl.handle.net/2117/1089152017-10-20T11:43:29ZLiu, ZhuangyiQuintanilla de Latorre, RamónThis note is devoted to the study of the time decay of the onedimensional dual-phase-lag thermoelasticity. In this theory two delay parameters tq and t¿ are proposed. It is known that the system is exponentially stable if tq < 2t¿ [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that tq = 2t¿ as well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper sub-interval of the spatial domain, when t¿ is spatially dependent.On the spatial behavior in two-temperature generalized thermoelastic theories
http://hdl.handle.net/2117/108910
On the spatial behavior in two-temperature generalized thermoelastic theories
Miranville, Alain; Quintanilla de Latorre, Ramón
This paper investigates the spatial behavior of the solutions of two generalized thermoelastic theories with two temperatures. To be more precise, we focus on the Green–Lindsay theory with two temperatures and the Lord–Shulman theory with two temperatures. We prove that a Phragmén–Lindelöf alternative of exponential type can be obtained in both cases. We also describe how to obtain a bound on the amplitude term by means of the boundary conditions for the Green–Lindsay theory with two temperatures.
The final publication is available at link.springer.com via https://doi.org/10.1007/s00033-017-0857-x
Fri, 20 Oct 2017 11:21:30 GMThttp://hdl.handle.net/2117/1089102017-10-20T11:21:30ZMiranville, AlainQuintanilla de Latorre, RamónThis paper investigates the spatial behavior of the solutions of two generalized thermoelastic theories with two temperatures. To be more precise, we focus on the Green–Lindsay theory with two temperatures and the Lord–Shulman theory with two temperatures. We prove that a Phragmén–Lindelöf alternative of exponential type can be obtained in both cases. We also describe how to obtain a bound on the amplitude term by means of the boundary conditions for the Green–Lindsay theory with two temperatures.On the viscoelastic mixtures of solids
http://hdl.handle.net/2117/108907
On the viscoelastic mixtures of solids
Fernández, Jose R.; Magaña Nieto, Antonio; Masid, Maria; Quintanilla de Latorre, Ramón
In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.
The final publication is available at link.springer.com via https://doi.org/10.1007/s00245-017-9439-8
Fri, 20 Oct 2017 10:49:05 GMThttp://hdl.handle.net/2117/1089072017-10-20T10:49:05ZFernández, Jose R.Magaña Nieto, AntonioMasid, MariaQuintanilla de Latorre, RamónIn this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.Stability for thermoelastic plates with two temperatures
http://hdl.handle.net/2117/108717
Stability for thermoelastic plates with two temperatures
Quintanilla de Latorre, Ramón; Racke, Reinhard
We investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations involving Schrödinger like equations, hyperbolic and elliptic equations, which have a different character compared to the classical one with the usual single temperature. Depending on the model -- with Fourier or with Cattaneo type heat conduction -- we obtain exponential resp. non-exponential stability, thus providing another examples where the change from Fourier's to Cattaneo's law leads to a loss of exponential stability.
Mon, 16 Oct 2017 11:24:49 GMThttp://hdl.handle.net/2117/1087172017-10-16T11:24:49ZQuintanilla de Latorre, RamónRacke, ReinhardWe investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations involving Schrödinger like equations, hyperbolic and elliptic equations, which have a different character compared to the classical one with the usual single temperature. Depending on the model -- with Fourier or with Cattaneo type heat conduction -- we obtain exponential resp. non-exponential stability, thus providing another examples where the change from Fourier's to Cattaneo's law leads to a loss of exponential stability.On the phase-lag with equation with spatial dependent lags
http://hdl.handle.net/2117/106377
On the phase-lag with equation with spatial dependent lags
Liu, Zhuangyi; Quintanilla de Latorre, Ramón; Wang, Yang
In this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.
Thu, 13 Jul 2017 11:42:19 GMThttp://hdl.handle.net/2117/1063772017-07-13T11:42:19ZLiu, ZhuangyiQuintanilla de Latorre, RamónWang, YangIn this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.On uniqueness and stability for a thermoelastic theory
http://hdl.handle.net/2117/105157
On uniqueness and stability for a thermoelastic theory
Quintanilla de Latorre, Ramón
In this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.
Tue, 06 Jun 2017 09:59:07 GMThttp://hdl.handle.net/2117/1051572017-06-06T09:59:07ZQuintanilla de Latorre, RamónIn this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.