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- M. C. Leseduarte, Ramón Quintanilla, Reinhard Racke
- Appl. Math. Lett.
- 2017

We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman model.

- M. C. Leseduarte, Ramón Quintanilla
- Asymptotic Analysis
- 2015

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… (More)

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 Hölder continuous dependence results on… (More)

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… (More)

- M. C. Leseduarte
- 2006

In what follows, we consider a theory for the behaviour of porous solids such that the matrix material is elastic and the interstices are void of material; it is a generalization of the classical theory of elasticity. The theory of porous elastic material has been established by Cowin andNunziato [2, 11]. In this theory, the bulk density is the product of… (More)

Let a be the topological graph shaped like the letter o . We denote by 0 the unique branching point of a , and by O and I the closures of the components of a \ {0} homeomorphics to the circle and the interval, respectively. A continuous map from a into itself satisfying that / has a fixed point in O, or / has a fixed point and /(0) € I is called a a map.… (More)

Abstract: 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… (More)

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… (More)

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