http://hdl.handle.net/2117/3339 2013-05-23T00:48:42Z 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. 2013-04-11T15:01:18Z 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. 2013-04-11T13:01:01Z 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. 2013-01-09T18:14:58Z http://hdl.handle.net/2117/17207 Title: A conserved phase-field system based on the Maxwell–Cattaneo law Authors: Miranville, Alain; Quintanilla de Latorre, Ramón Abstract: Our aim in this paper is to study a generalization of the conserved Caginalp phasefield system based on the Maxwell–Cattaneo law for heat conduction and endowed with Neumann boundary conditions. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. 2013-01-08T11:33:15Z http://hdl.handle.net/2117/16847 Title: Non-linear deformations of porous elastic solids Authors: Iesan, Dorin; Quintanilla de Latorre, Ramón Abstract: This paper is concerned with the non-linear theory of porouselastic bodies. First, we present the basic equations in general curvilinear coordinates. The constitutive equations for porouselastic bodies with incompressible matrix material are derived. Then, the equilibrium theory is investigated. An existence result within the one-dimensional theory is presented. The theory is applied in order to study the torsion of an isotropic circular cylinder and the flexure of a cuboid made of an anisotropic material. It is shown that the equations of equilibrium reduce to a single ordinary differential equation governing an unknown function which characterizes the aforementioned deformations. 2012-11-06T16:00:27Z http://hdl.handle.net/2117/16720 Title: Phragmén-Lindelöf alternative for an exact heat conduction equation with delay Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón Abstract: In this paper we investigate the spatial behavior of the solutions for a theory for the heat conduction with one delay term. We obtain a Phragm én- Lindelöf type alternative. That is, the solutions either decay in an exponential way or blow-up at in nity in an exponential way. We also show how to obtain an upper bound for the amplitude term. Later we point out how to extend the results to a thermoelastic problem. We nish the paper by considering the equation obtained by the Taylor approximation to the delay term. A Phragm én-Lindelöf type alternative is obtained for the forward and backward in time equations. 2012-10-11T14:06:43Z http://hdl.handle.net/2117/16197 Title: On uniqueness and continuous dependence in type III thermoelasticity Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón Abstract: This note is concerned with the linear (and linearised) type III thermoelastic theory proposed by Green and Naghdi. First, the continuous dependence of the solutions upon the initial data and supply terms is established for noncentrosymmetric bodies. Then a uniqueness result for centrosymmetric materials is established. 2012-07-09T08:37:37Z http://hdl.handle.net/2117/16064 Title: Further mathematical results concerning Burgers fluids and their generalizations Authors: Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam Abstract: In this paper, we extend the earlier work by Quintanilla and Rajagopal (Math Methods Appl Sci 29: 2133–2147, 2006) and establish qualitative new results for a proper generalization of Burgers’ original work that stems form a general thermodynamic framework. Such fluids have been used to describe the behavior of several geological materials such as asphalt and the earth’s mantle as well as polymeric fluids. We study questions concerning stability, uniqueness and continuous dependence on initial data for the solutions of the flows of these fluids. We show that if certain conditions are not satisfied by the material moduli, the solutions could be unstable. The spatial behavior of the solutions is also analyzed. 2012-06-15T18:08:32Z http://hdl.handle.net/2117/16054 Title: Analyticity in porous-thermoelasticity with microtemperatures Authors: Pamplona, Paulo Xavier; Muñoz Rivera, Jaime E.; Quintanilla de Latorre, Ramón Abstract: In this note we study the analyticity of the solutions to the one-dimensional porouselasticity problem with temperatures and microtemperatures when viscoelasticity and porous viscosity effects are also present. We show the lack of analyticity when the porous dissipation is weak, and the analyticity when it is strong 2012-06-15T16:02:55Z http://hdl.handle.net/2117/12300 Title: Mathematical results concerning a class of incompressible viscoelastic solids of differential type Authors: Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam Abstract: In this paper we investigate several mathematical aspects concerning a class of incompressible viscoelastic solids of the differential type. The model that we consider can be viewed as a generalization of the Kelvin—Voigt viscoelastic solid. We obtain a uniqueness result and show that when the shear modulus of the viscoelastic solid is positive the solutions decay exponentially. We also show that if the shear modulus is negative, a physically unacceptable situation, we have exponential growth of the solutions, which is in keeping with physical expectations. The impossibility of localization of the solutions in finite time is also proved. The last section is devoted to the development of spatial decay estimates in the quasi-static case. 2011-04-07T14:29:35Z http://hdl.handle.net/2117/12002 Title: On the decay of solutions for porous-elastic systems with history Authors: Pamplona, Paulo Xavier; Muñoz Rivera, Jaime E.; Quintanilla de Latorre, Ramón Abstract: In this paper we study the asymptotic behavior to an one-dimensional porous-elasticity problem with history. We show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent. And we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present. 2011-03-21T16:45:35Z http://hdl.handle.net/2117/10745 Title: A Phase-field model based on a three-phase-lag heat conduction Authors: Miranville, Alain; Quintanilla de Latorre, Ramón Abstract: Our aim in this article is to study a phase-field system based on a three-phase-lag for the termal flux vector. In particular, we prove the existence and uniqueness of solutions and then study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist. 2010-12-23T19:34:00Z http://hdl.handle.net/2117/10516 Title: Decay of solutions in nonsimple thermoelastic bars Authors: Fernández-Sare, Hugo; Muñoz Rivera, Jaime E.; Quintanilla de Latorre, Ramón Abstract: In this paper we investigate the asymptotic behavior of the semigroup associated to the solutions of the initial boundary value problem for a one-dimensional nonsimple thermoelastic solids. We show that the semigroup is exponentially stable but is not analytic. Moreover we show the impossibility of time localization of the solutions. 2010-12-09T18:55:28Z http://hdl.handle.net/2117/8764 Title: Energy decay rate of a mixed type II and type III thermoelastic system Authors: Liu, Zhuangyi; Quintanilla de Latorre, Ramón Abstract: In this paper, we study the energy decay rate for a mixed type II and type III thermoelastic system. The system consist of a wave equation and a heat equation of type II in another part of the domain, coupled in certain pattern. When the damping coefficient function satisfies certain conditions at the interface, a polynomial type decay rate is obtained. This result is proved by verifying the frequency domain conditions. 2010-09-06T14:35:11Z http://hdl.handle.net/2117/8763 Title: A note on a non-standard problem for an equation with a delay term Authors: Quintanilla de Latorre, Ramón Abstract: In this note we investigate the continuous dependence of the solutions for a theory of heat conduction with a delay term. We use energy arguments to obtain the continuous dependence results and spectral arguments to prove the non-uniqueness result. The extension to the thermoelastic problem is also pointed out. 2010-09-06T14:18:04Z