DSpace Collection:
http://hdl.handle.net/2117/3339
Wed, 04 Mar 2015 23:01:58 GMT2015-03-04T23:01:58Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoOn the asymptotic spatial behaviour of the solutions of the nerve system
http://hdl.handle.net/2117/26512
Title: On the asymptotic spatial behaviour of the solutions of the nerve system
Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Abstract: In this paper we investigate the asymptotic spatial behavior of the solutions for several models for the nerve fibers.
First, our analysis deals with the coupling of two parabolic equations. We prove that, under suitable assumptions on the coefficients
and the nonlinear function, the decay is similar to the one corresponding to the heat equation. A limit case of this system
corresponds to the coupling of a parabolic equation with an ordinary differential equation. In this situation, we see that for suitable
boundary conditions the solution ceases to exist for a finite value of the spatial variable. Next two sections correspond to
the coupling of a hyperbolic/parabolic and hyperbolic/ordinary differential problems. For the first one we obtain that the decay
is like an exponential of a second degree polynomial in the spatial variable. In the second one, we prove a similar behaviour to
the one corresponding to the wave equation. In these two sections we use in a relevant way an exponentially weighted Poincaré
inequality which has been revealed very useful in several thermal and mechanical problems. This kind of results have relevance
to understand the propagation of perturbations for nerve models.Wed, 25 Feb 2015 14:52:52 GMThttp://hdl.handle.net/2117/265122015-02-25T14:52:52ZLeseduarte Milán, María Carme; Quintanilla de Latorre, RamónnoNerve equation, Spatial decay, Estimates, Spatial nonexistence, FitzHugh–NagumoIn this paper we investigate the asymptotic spatial behavior of the solutions for several models for the nerve fibers.
First, our analysis deals with the coupling of two parabolic equations. We prove that, under suitable assumptions on the coefficients
and the nonlinear function, the decay is similar to the one corresponding to the heat equation. A limit case of this system
corresponds to the coupling of a parabolic equation with an ordinary differential equation. In this situation, we see that for suitable
boundary conditions the solution ceases to exist for a finite value of the spatial variable. Next two sections correspond to
the coupling of a hyperbolic/parabolic and hyperbolic/ordinary differential problems. For the first one we obtain that the decay
is like an exponential of a second degree polynomial in the spatial variable. In the second one, we prove a similar behaviour to
the one corresponding to the wave equation. In these two sections we use in a relevant way an exponentially weighted Poincaré
inequality which has been revealed very useful in several thermal and mechanical problems. This kind of results have relevance
to understand the propagation of perturbations for nerve models.Foreword to special issue on ‘‘Qualitative Methods in Engineering Science’’
http://hdl.handle.net/2117/26438
Title: Foreword to special issue on ‘‘Qualitative Methods in Engineering Science’’
Authors: Quintanilla de Latorre, Ramón; Fu, YibinThu, 19 Feb 2015 16:17:32 GMThttp://hdl.handle.net/2117/264382015-02-19T16:17:32ZQuintanilla de Latorre, Ramón; Fu, YibinnoPhase-lag heat conduction: decay rates for limit problems and well-posedness
http://hdl.handle.net/2117/26420
Title: Phase-lag heat conduction: decay rates for limit problems and well-posedness
Authors: Borgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, Reinhard
Abstract: In two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.Wed, 18 Feb 2015 17:18:03 GMThttp://hdl.handle.net/2117/264202015-02-18T17:18:03ZBorgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, ReinhardnoHyperbolic models in heat conduction, Stability, Generalized thermoelasticity, Qualitative aspects, Stability, Waves, ModelIn two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.Hölder stability in type III thermoelastodynamics
http://hdl.handle.net/2117/26416
Title: Hölder stability in type III thermoelastodynamics
Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Abstract: This note is concerned with the linear (and linearized) Type III thermoelastodynamic theory proposed by Green and Naghdi. We here assume that the mass density is positive and the thermal conductivity tensor is positive definite. However, we do not assume the positivity of any other tensor. In this situation, we obtain Holder continuous dependence results on the supply terms. We also sketch how to prove the continuous dependence on the initial data.
Description: Electronic version of an article published as "Archive of applied mechanics", vol. 84 nº 9-11, October 2014, p. 1465-1476. DOI No 10.1007/s00419-014-0827-0.Wed, 18 Feb 2015 15:34:37 GMThttp://hdl.handle.net/2117/264162015-02-18T15:34:37ZLeseduarte Milán, María Carme; Quintanilla de Latorre, RamónnoType III thermoelastodynamics, Hölder stability, Continuous dependence on initial data and supply terms, Lagrange identities methodThis note is concerned with the linear (and linearized) Type III thermoelastodynamic theory proposed by Green and Naghdi. We here assume that the mass density is positive and the thermal conductivity tensor is positive definite. However, we do not assume the positivity of any other tensor. In this situation, we obtain Holder continuous dependence results on the supply terms. We also sketch how to prove the continuous dependence on the initial data.Spatial behavior in phase-lag heat conduction
http://hdl.handle.net/2117/26266
Title: Spatial behavior in phase-lag heat conduction
Authors: Quintanilla de Latorre, Ramón; Racke, Reinhard
Abstract: 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. Depending on the relative order of derivation, with respect to the time, we propose different arguments. One is inspired by the arguments for parabolic problems and the other is inspired by the arguments for hyperbolic problems. In the first case, we obtain a Phragmén-Lindelöf alternative for the solutions. In the second case, we obtain an estimate for the decay as well as a domain of influence result. The main tool to manage these problems is the use of an exponentially weighted Poincaré inequality.Mon, 09 Feb 2015 13:45:15 GMThttp://hdl.handle.net/2117/262662015-02-09T13:45:15ZQuintanilla de Latorre, Ramón; Racke, ReinhardnoModels in heat conduction, Spatial stability, Domain of influence, Saint-Venant's principleIn 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. Depending on the relative order of derivation, with respect to the time, we propose different arguments. One is inspired by the arguments for parabolic problems and the other is inspired by the arguments for hyperbolic problems. In the first case, we obtain a Phragmén-Lindelöf alternative for the solutions. In the second case, we obtain an estimate for the decay as well as a domain of influence result. The main tool to manage these problems is the use of an exponentially weighted Poincaré inequality.Analysis of the equations governing the motion of a degrading elastic solid due to diffusion of a fluid
http://hdl.handle.net/2117/24474
Title: Analysis of the equations governing the motion of a degrading elastic solid due to diffusion of a fluid
Authors: Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam
Abstract: Degradation of solids bearing load due to the infusion of moisture when exposed to the environment
can leads to a decrease in their load carrying capacity and can also lead to the failure of the body from
performing its intended task. In this short paper, we study some qualitative properties of the solution
to systems of equations that describe the degradation in a linearized elastic solid due to the diffusion
of a fluid. The model that is considered allows for the material properties of the solid to depend on the
concentration of the diffusing fluid. While the load carrying capacity of a solid could decrease or increase
due to the infusion of a fluid, we consider the case when degradation takes place. We are able to obtain
results concerning the uniqueness of solutions to the problem under consideration. We also consider
special anti-plane and quasi-static deformations of the body.
Description: Electronic version of an article published as "IMA Journal of applied mathematics", vol. 79, no 5, 2014, p. 778-789. DOI: 10.1093/imamat/hxt050 <http://imamat.oxfordjournals.org/content/79/5/778.abstract>Fri, 24 Oct 2014 16:30:54 GMThttp://hdl.handle.net/2117/244742014-10-24T16:30:54ZQuintanilla de Latorre, Ramón; Rajagopal, KumbakonamnoDegradation, Diffusion, Constitutive relations, Uniqueness, Ani-plane strainDegradation of solids bearing load due to the infusion of moisture when exposed to the environment
can leads to a decrease in their load carrying capacity and can also lead to the failure of the body from
performing its intended task. In this short paper, we study some qualitative properties of the solution
to systems of equations that describe the degradation in a linearized elastic solid due to the diffusion
of a fluid. The model that is considered allows for the material properties of the solid to depend on the
concentration of the diffusing fluid. While the load carrying capacity of a solid could decrease or increase
due to the infusion of a fluid, we consider the case when degradation takes place. We are able to obtain
results concerning the uniqueness of solutions to the problem under consideration. We also consider
special anti-plane and quasi-static deformations of the body.On a theory of thermoelastic materials with double porosity structure
http://hdl.handle.net/2117/24346
Title: On a theory of thermoelastic materials with double porosity structure
Authors: Iesan, Dorin; Quintanilla de Latorre, Ramón
Abstract: In this article, we use the Nunziato–Cowin theory of materials with voids to derive a theory of thermoelastic solids, which have a double porosity structure. The new theory is not based on Darcy's law. In the case of equilibrium, in contrast with the classical theory of elastic materials with double porosity, the porosity structure of the body is influenced by the displacement field. We prove the uniqueness of solutions by means of the logarithmic convexity arguments as well as the instability of solutions whenever the internal energy is not positive definite. Later, we use semigroup arguments to prove the existence of solutions in the case that the internal energy is positive. The deformation of an elastic space with a spherical cavity is investigated.
Description: Electronic version of an article published as "Journal of thermal stresses", vol. 37, no 9, 2014, p. 1017-1036. DOI: 10.1080/01495739.2014.914776 <http://www.tandfonline.com/doi/abs/10.1080/01495739.2014.914776#.VDf2nRbQo5h>Fri, 10 Oct 2014 16:05:00 GMThttp://hdl.handle.net/2117/243462014-10-10T16:05:00ZIesan, Dorin; Quintanilla de Latorre, RamónnoExistence and uniqueness results, Instability, Porous thermoelastic solids, Unbounded medium with a cavityIn this article, we use the Nunziato–Cowin theory of materials with voids to derive a theory of thermoelastic solids, which have a double porosity structure. The new theory is not based on Darcy's law. In the case of equilibrium, in contrast with the classical theory of elastic materials with double porosity, the porosity structure of the body is influenced by the displacement field. We prove the uniqueness of solutions by means of the logarithmic convexity arguments as well as the instability of solutions whenever the internal energy is not positive definite. Later, we use semigroup arguments to prove the existence of solutions in the case that the internal energy is positive. The deformation of an elastic space with a spherical cavity is investigated.On the backward in time problem for the thermoelasticity with two temperatures
http://hdl.handle.net/2117/23165
Title: On the backward in time problem for the thermoelasticity with two temperatures
Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Abstract: This paper is devoted to the study of the existence, uniqueness, continuous dependence and spatial behaviour of the solutions for the backward in time problem determined by the Type III with two temperatures thermoelastodynamic theory. We first show the existence, uniqueness and continuous dependence of the solutions. Instability of the solutions for the Type II with two temperatures theory is proved later. For the one-dimensional Type III with two temperatures theory, the exponential instability is also pointed-out. We also analyze the spatial behaviour of the solutions. By means of the exponentially weighted Poincare inequality, we are able to obtain a function that defines a measure on the solutions and, therefore, we obtain the usual exponential type alternative for the solutions of the problem defined in a semi-infinite cylinder.
Description: Electronic version of an article published as "Discrete and continuous dynamical series", vol. 19, no 3, May 2014, p. 679-695. DOI 10.3934/dcdsb.2014.19.679.Thu, 05 Jun 2014 13:19:17 GMThttp://hdl.handle.net/2117/231652014-06-05T13:19:17ZLeseduarte Milán, María Carme; Quintanilla de Latorre, RamónnoBackward in time problem, Type III with two temperatures thermoelasticity, existence, continuous dependence, spatial growth/decay of solutions, energy arguments, WELL-POSED PROBLEM, ENERGY-DISSIPATION, CONTINUOUS DEPENDENCE, HEAT-CONDUCTION, SPATIAL DECAY, TEMPERATURE THERMOELASTICITY, UNIQUENESS, STABILITY, PROPAGATION, BOUNDARYThis paper is devoted to the study of the existence, uniqueness, continuous dependence and spatial behaviour of the solutions for the backward in time problem determined by the Type III with two temperatures thermoelastodynamic theory. We first show the existence, uniqueness and continuous dependence of the solutions. Instability of the solutions for the Type II with two temperatures theory is proved later. For the one-dimensional Type III with two temperatures theory, the exponential instability is also pointed-out. We also analyze the spatial behaviour of the solutions. By means of the exponentially weighted Poincare inequality, we are able to obtain a function that defines a measure on the solutions and, therefore, we obtain the usual exponential type alternative for the solutions of the problem defined in a semi-infinite cylinder.On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity
http://hdl.handle.net/2117/21495
Title: On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity
Authors: Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
Abstract: This paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.Mon, 10 Feb 2014 14:06:59 GMThttp://hdl.handle.net/2117/214952014-02-10T14:06:59ZMagaña Nieto, Antonio; Quintanilla de Latorre, RamónnoMicropolar thermoviscoelasticity, Uniqueness, Analyticity, Exponential decayThis paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.On the spatial behavior in type III thermoelastodynamics
http://hdl.handle.net/2117/21453
Title: On the spatial behavior in type III thermoelastodynamics
Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Abstract: This note is concerned with the linear (and linearized) Type III thermoelastodynamic theory proposed by Green and Naghdi. We investigate the spatial behavior of the solutions when we assume the positivity of the elasticity tensor, the thermal conductivity tensor, the mass density and the heat capacity. However, we do not assume (a priori) the positivity of the internal energy. We first obtain a Phragmén-Lindelöf alternative of exponential type for the solutions. Later, we prove that the decay can be controlled by the exponential of a second-degree polynomial. This is similar to other thermoelastic situations.Tue, 04 Feb 2014 16:20:58 GMThttp://hdl.handle.net/2117/214532014-02-04T16:20:58ZLeseduarte Milán, María Carme; Quintanilla de Latorre, RamónnoType III thermoelastodynamics, Spatial growth/decay of solutions, Energy methods, Comparison argumentsThis note is concerned with the linear (and linearized) Type III thermoelastodynamic theory proposed by Green and Naghdi. We investigate the spatial behavior of the solutions when we assume the positivity of the elasticity tensor, the thermal conductivity tensor, the mass density and the heat capacity. However, we do not assume (a priori) the positivity of the internal energy. We first obtain a Phragmén-Lindelöf alternative of exponential type for the solutions. Later, we prove that the decay can be controlled by the exponential of a second-degree polynomial. This is similar to other thermoelastic situations.Spatial decay for several phase-field models
http://hdl.handle.net/2117/20931
Title: Spatial decay for several phase-field models
Authors: Miranville, Alain; Quintanilla de Latorre, Ramón
Abstract: In this paper, we study the spatial behavior of three phase-field models. First, we consider the Cahn-Hilliard equation and
we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal
phase-field equation (i.e., the Allen-Cahn equation), we prove the nonexistence and the fast decay of solutions and, for
the nonisothermal case governed by the Fourier law, we obtain a Phragm ́
en-Lindel ̈
of alternative of exponential type,
respectively.Thu, 05 Dec 2013 15:30:33 GMThttp://hdl.handle.net/2117/209312013-12-05T15:30:33ZMiranville, Alain; Quintanilla de Latorre, RamónnoPhase-field models, Spatial decay, Exponential decay, Fast decay, Phragmén-Lindelöf alternativeIn this paper, we study the spatial behavior of three phase-field models. First, we consider the Cahn-Hilliard equation and
we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal
phase-field equation (i.e., the Allen-Cahn equation), we prove the nonexistence and the fast decay of solutions and, for
the nonisothermal case governed by the Fourier law, we obtain a Phragm ́
en-Lindel ̈
of alternative of exponential type,
respectively.Decay of solutions for a mixture of thermoelastic one dimensional solids
http://hdl.handle.net/2117/19560
Title: Decay of solutions for a mixture of thermoelastic one dimensional solids
Authors: Muñoz Rivera, Jaime E.; Naso, Maria-Grazia; Quintanilla de Latorre, Ramón
Abstract: We study a PDE system modeling thermomechanical deformations for a mixture of thermoelastic solids. In particular we investigate the asymptotic behavior of the solutions. First, we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent. Subsequently, we find the necessary and sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate.Mon, 17 Jun 2013 16:52:48 GMThttp://hdl.handle.net/2117/195602013-06-17T16:52:48ZMuñoz Rivera, Jaime E.; Naso, Maria-Grazia; Quintanilla de Latorre, RamónnoWe study a PDE system modeling thermomechanical deformations for a mixture of thermoelastic solids. In particular we investigate the asymptotic behavior of the solutions. First, we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent. Subsequently, we find the necessary and sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate.On the decay of solutions for the heat conduction with two temperatures
http://hdl.handle.net/2117/18775
Title: On the decay of solutions for the heat conduction with two temperatures
Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Abstract: This paper is devoted to the study of the asymptotic behavior of the solutions of the system of
equations that models the heat conduction with two temperatures. That is, we consider a mixture of isotropic
and homogeneous rigid solids. We analyze the static problem in a semi-infinite cylinder where every material
point has two temperatures with nonlinear boundary conditions on the lateral side. A Phragmén–Lindelöf
alternative for the solutions is obtained by means of energy arguments. Estimates for the decay and growth of
the solutions are presented. We also prove that the only solution vanishing in the exterior of a bounded set is
the null solution for a particular subfamily of problems. Cone-like domains are considered in the last section,
and we obtain decay estimates for the solutions when the total energy is bounded.Thu, 11 Apr 2013 15:01:18 GMThttp://hdl.handle.net/2117/187752013-04-11T15:01:18ZLeseduarte Milán, María Carme; Quintanilla de Latorre, RamónnoThis paper is devoted to the study of the asymptotic behavior of the solutions of the system of
equations that models the heat conduction with two temperatures. That is, we consider a mixture of isotropic
and homogeneous rigid solids. We analyze the static problem in a semi-infinite cylinder where every material
point has two temperatures with nonlinear boundary conditions on the lateral side. A Phragmén–Lindelöf
alternative for the solutions is obtained by means of energy arguments. Estimates for the decay and growth of
the solutions are presented. We also prove that the only solution vanishing in the exterior of a bounded set is
the null solution for a particular subfamily of problems. Cone-like domains are considered in the last section,
and we obtain decay estimates for the solutions when the total energy is bounded.On the logarithmic convexity in thermoelastiscity with microtemperatures
http://hdl.handle.net/2117/18770
Title: On the logarithmic convexity in thermoelastiscity with microtemperatures
Authors: Quintanilla de Latorre, Ramón
Abstract: This article is concerned with the linear theory of thermoelasticity with
microtemperatures. In a recent article we have used the logarithmic convexity method
to investigate uniqueness, instability and structural stability. The results are restricted
to the case when the constitutive coefficients
k1 and k3 have the same signs. Here we
prove that these results also hold when the coefficients k1 and k3 have opposite signs.Thu, 11 Apr 2013 13:01:01 GMThttp://hdl.handle.net/2117/187702013-04-11T13:01:01ZQuintanilla de Latorre, RamónnoThis article is concerned with the linear theory of thermoelasticity with
microtemperatures. In a recent article we have used the logarithmic convexity method
to investigate uniqueness, instability and structural stability. The results are restricted
to the case when the constitutive coefficients
k1 and k3 have the same signs. Here we
prove that these results also hold when the coefficients k1 and k3 have opposite signs.On a strain gradient theory of thermoviscoelasticity
http://hdl.handle.net/2117/17245
Title: On a strain gradient theory of thermoviscoelasticity
Authors: Iesan, Dorin; Quintanilla de Latorre, Ramón
Abstract: This paper is concerned with a strain gradient theory of thermoviscoelasticity in which the time derivatives of the strain tensors are included in the set of independent constitutive variables. The theory is motivated by the recent interest in the study of gradient theories. First, we establish the basic equations of the linear theory and present two uniqueness results. Then, we use a semigroup approach to derive an existence result. Finally, we establish the constitutive equations for an isotropic chiral material and derive a solution of the field equations.Wed, 09 Jan 2013 18:14:58 GMThttp://hdl.handle.net/2117/172452013-01-09T18:14:58ZIesan, Dorin; Quintanilla de Latorre, RamónnoThis paper is concerned with a strain gradient theory of thermoviscoelasticity in which the time derivatives of the strain tensors are included in the set of independent constitutive variables. The theory is motivated by the recent interest in the study of gradient theories. First, we establish the basic equations of the linear theory and present two uniqueness results. Then, we use a semigroup approach to derive an existence result. Finally, we establish the constitutive equations for an isotropic chiral material and derive a solution of the field equations.