Articles de revista
http://hdl.handle.net/2117/3339
Thu, 03 Sep 2015 06:57:34 GMT2015-09-03T06:57:34ZOn the time decay of solutions in micropolar viscoelasticity
http://hdl.handle.net/2117/76207
On the time decay of solutions in micropolar viscoelasticity
Leseduarte Milán, María Carme; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with isotropic micropolar viscoelastic materials.
It can be said that that kind of materials have two internal structures: the
macrostructure, where the elasticity effects are noticed, and the microstructure,
where the polarity of the material points allows them to rotate. We introduce,
step by step, dissipation mechanisms in both structures, obtain the corresponding
system of equations and determine the behavior of its solutions with respect the
time.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11012-015-0117-0
Wed, 01 Jul 2015 00:00:00 GMThttp://hdl.handle.net/2117/762072015-07-01T00:00:00ZA generalization of the Allen–Cahn equation
http://hdl.handle.net/2117/27478
A generalization of the Allen–Cahn equation
Miranville, Alain; Quintanilla de Latorre, Ramón
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 systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record: Miranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430 is available online at:http://imamat.oxfordjournals.org/content/80/2/410.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2117/274782015-04-01T00:00:00ZLower bounds of end effects for a nonhomogeneous isotropic linear elastic solid in anti-plane shear
http://hdl.handle.net/2117/26875
Lower bounds of end effects for a nonhomogeneous isotropic linear elastic solid in anti-plane shear
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this paper we give lower bounds for the spatial decay of the solutions for anti-plane shear deformations in the case of
isotropic inhomogeneous elastic materials. We first consider the case when the shear modulus only depends on the lateral
direction. By means of the logarithmic convexity arguments we obtain the required estimates. Some pictures illustrate
our results. We also study the general inhomogeneity. We give some lower bounds whenever shear modulus
satisfies several requirements.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/2117/268752015-02-01T00:00:00ZSpatial stability in linear thermoelasticity
http://hdl.handle.net/2117/26874
Spatial stability in linear thermoelasticity
Knops, Robin J.; Quintanilla de Latorre, Ramón
Uniqueness and spatial stability are investigated for smooth solutions to boundary value
problems in non-classical linearised and linear thermoelasticity subject to certain conditions
on material coefficients. Uniqueness is derived for standard boundary conditions
on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed
for the semi-infinite prismatic cylinder in the absence of specified axial asymptotic
behaviour. Alternative growth and decay estimates are established principally for the
cross-sectional energy flux that is shown to satisfy a first order differential inequality.
Uniqueness in the class of solutions with bounded energy follows as a corollary.
Separate discussion is required for the linearised and linear theories. Although the general
approach is similar for both theories, the argument must be considerably modified for
the treatment of the linear theory.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/2117/268742015-03-01T00:00:00ZOn the asymptotic spatial behaviour of the solutions of the nerve system
http://hdl.handle.net/2117/26512
On the asymptotic spatial behaviour of the solutions of the nerve system
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
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.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/2117/265122015-03-01T00:00:00ZForeword to special issue on ‘‘Qualitative Methods in Engineering Science’’
http://hdl.handle.net/2117/26438
Foreword to special issue on ‘‘Qualitative Methods in Engineering Science’’
Quintanilla de Latorre, Ramón; Fu, Yibin
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/2117/264382015-03-01T00:00:00ZPhase-lag heat conduction: decay rates for limit problems and well-posedness
http://hdl.handle.net/2117/26420
Phase-lag heat conduction: decay rates for limit problems and well-posedness
Borgmeyer, Karin; Quintanilla de Latorre, Ramón; Racke, Reinhard
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.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.
Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/2117/264202014-12-01T00:00:00ZHölder stability in type III thermoelastodynamics
http://hdl.handle.net/2117/26416
Hölder stability in type III thermoelastodynamics
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
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.
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, 01 Oct 2014 00:00:00 GMThttp://hdl.handle.net/2117/264162014-10-01T00:00:00ZSpatial behavior in phase-lag heat conduction
http://hdl.handle.net/2117/26266
Spatial behavior in phase-lag heat conduction
Quintanilla de Latorre, Ramón; Racke, Reinhard
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.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/2117/262662015-03-01T00:00:00ZAnalysis of the equations governing the motion of a degrading elastic solid due to diffusion of a fluid
http://hdl.handle.net/2117/24474
Analysis of the equations governing the motion of a degrading elastic solid due to diffusion of a fluid
Quintanilla de Latorre, Ramón; Rajagopal, Kumbakonam
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.
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>
Wed, 01 Oct 2014 00:00:00 GMThttp://hdl.handle.net/2117/244742014-10-01T00:00:00Z