Articles de revista
http://hdl.handle.net/2117/3339
Wed, 02 Dec 2015 05:54:17 GMT2015-12-02T05:54:17ZSpatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section
http://hdl.handle.net/2117/78647
Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section
Knops, Robin J.; Quintanilla de Latorre, Ramón
Alternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination
of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-015-9523-8
Mon, 02 Nov 2015 14:30:12 GMThttp://hdl.handle.net/2117/786472015-11-02T14:30:12ZKnops, Robin J.Quintanilla de Latorre, RamónAlternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination
of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.Spatial behavior for solutions in heat conduction with two delays
http://hdl.handle.net/2117/77992
Spatial behavior for solutions in heat conduction with two delays
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
In this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.
Tue, 20 Oct 2015 15:32:43 GMThttp://hdl.handle.net/2117/779922015-10-20T15:32:43ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn this note, we investigate the spatial behavior of the solutions of the equation proposed to describe a theory for the heat conduction with two delay terms. We obtain an alternative of the Phragmén-Lindelöf type, which means that the solutions either decay or blow-up at infinity, both options in an exponential way. We also describe how to obtain an upper bound for the amplitude term. This is the first contribution on spatial behavior for partial differential equations involving two delay terms. We use energy arguments. The main point of the contribution is the use of an exponentially weighted energy function.On 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
Mon, 20 Jul 2015 07:18:57 GMThttp://hdl.handle.net/2117/762072015-07-20T07:18:57ZLeseduarte Milán, María CarmeMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis 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.A 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.
Tue, 21 Apr 2015 13:31:16 GMThttp://hdl.handle.net/2117/274782015-04-21T13:31:16ZMiranville, AlainQuintanilla de Latorre, RamónOur 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.Lower 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.
Thu, 19 Mar 2015 18:59:40 GMThttp://hdl.handle.net/2117/268752015-03-19T18:59:40ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn 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.Spatial 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.
Thu, 19 Mar 2015 18:33:43 GMThttp://hdl.handle.net/2117/268742015-03-19T18:33:43ZKnops, Robin J.Quintanilla de Latorre, RamónUniqueness 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.On 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.
Wed, 25 Feb 2015 14:52:52 GMThttp://hdl.handle.net/2117/265122015-02-25T14:52:52ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónIn 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
Foreword to special issue on ‘‘Qualitative Methods in Engineering Science’’
Quintanilla de Latorre, Ramón; Fu, Yibin
Thu, 19 Feb 2015 16:17:32 GMThttp://hdl.handle.net/2117/264382015-02-19T16:17:32ZQuintanilla de Latorre, RamónFu, YibinPhase-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.
Wed, 18 Feb 2015 17:18:03 GMThttp://hdl.handle.net/2117/264202015-02-18T17:18:03ZBorgmeyer, KarinQuintanilla de Latorre, RamónRacke, ReinhardIn 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
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, 18 Feb 2015 15:34:37 GMThttp://hdl.handle.net/2117/264162015-02-18T15:34:37ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónThis 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.