Now showing items 1-17 of 17

    • A Caginalp phase-field system based on type III heat conduction with two temperatures 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2016-06-01)
      Article
      Open Access
      Our aim in this paper is to study a generalization of the Caginalp phasefield system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness ...
    • A Caginalp phase-field system with a nonlinear coupling 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2010-08-01)
      Article
      Restricted access - publisher's policy
      Our aim in this article is to study a Caginalp phase-field system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi (called type III thermoelasticity) and with a nonlinear coupling. ...
    • A conserved phase-field system based on the Maxwell–Cattaneo law 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2013-06-01)
      Article
      Restricted access - publisher's policy
      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 ...
    • A generalization of the Allen–Cahn equation 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2015-04-01)
      Article
      Open Access
      Our aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic ...
    • A generalization of the Caginalp phase-field system based on the Cattaneo law 

      Miranville, Alain; Quintanilla de Latorre, Ramón (Elsevier, 2009)
      Article
      Restricted access - publisher's policy
      We consider in this article a generalization of the Caginalp model for phase transitions based on the Maxwell Cattaneo law, instead of the classical Fourier law. In particular, we prove the existence and uniqueness of ...
    • A Phase-field model based on a three-phase-lag heat conduction 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2011-02-01)
      Article
      Restricted access - publisher's policy
      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 ...
    • Asymptotic behavior of a Cahn-Hilliard/Allen-Cahn system with temperature 

      Miranville, Alain; Quintanilla de Latorre, Ramón; Saoud, Wafa (2020-04)
      Article
      Open Access
      The main goal of this paper is to study the asymptotic behavior of a coupled Cahn-Hilliard/Allen-Cahn system with temperature. The work is divided into two parts: In the rst part, the heat equation is based on the usual ...
    • Exponential decay in one-dimensional type III thermoelasticity with voids 

      Miranville, Alain; Quintanilla de Latorre, Ramón (Elsevier, 2019-08)
      Article
      Open Access
      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 ...
    • Exponential decay of solutions in type II porous-thermo-elasticity with quasi-static microvoids 

      Magaña Nieto, Antonio; Miranville, Alain; Quintanilla de Latorre, Ramón (2020-12-15)
      Article
      Restricted access - publisher's policy
      In this note we study the problem proposed by the one-dimensional thermo-porous-elasticity of type II with quasi-static microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so ...
    • Exponential stability in type II thermoviscoelasticity with voids 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2020-04)
      Article
      Restricted access - publisher's policy
      In this paper we consider the one-dimensional type II thermoviscoelastic 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 ...
    • On a Caginalp phase-field system with two temperatures and memory 

      Conti, Monica; Gatti, Stefania; Miranville, Alain; Quintanilla de Latorre, Ramón (2017-06)
      Article
      Open Access
      The Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law ...
    • On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2016-10-31)
      Article
      Open Access
      Our aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase-¿eld systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain ...
    • On the spatial behavior in two-temperature generalized thermoelastic theories 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2017-10-01)
      Article
      Open Access
      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 ...
    • On the stability in phase-lag heat conduction with two temperatures 

      Magaña Nieto, Antonio; Miranville, Alain; Quintanilla de Latorre, Ramón (2018-06-15)
      Article
      Open Access
      We investigate the well-posedness and the stability of the solutions for several Taylor approximations of the phase-lag two-temperature equations.We give conditions on the parameters which guarantee the existence and ...
    • On the time decay in phase-lag thermoelasticity with two temperatures 

      Magaña Nieto, Antonio; Miranville, Alain; Quintanilla de Latorre, Ramón (AMER INST MATHEMATICAL SCIENCES-AIMS, 2019-09-12)
      Article
      Open Access
      The aim of this paper is to study the time decay of the solutions for two models of the one-dimensional phase-lag thermoelasticity with two temperatures. The first one is obtained when the heat flux vector and the inductive ...
    • Some generalizations of the Caginalp phase-field system 

      Quintanilla de Latorre, Ramón; Miranville, Alain (Taylor and Francis, 2009-06)
      Article
      Restricted access - publisher's policy
      Our aim in this article is to study generalizations of the Caginalp phasefield system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi. In particular, we obtain well-posedness results ...
    • Spatial decay for several phase-field models 

      Miranville, Alain; Quintanilla de Latorre, Ramón (2013-10)
      Article
      Restricted access - publisher's policy
      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 ...