Analyticity of Semigroups Associated with Thermoviscoelastic Mixtures of Solids

Exponential stability in thermoviscoelastic mixtures of solids

“…In this paper we want to emphasize the study of the decay of solutions to the case of a one-dimensional beam composed by a mixture of two thermoviscoelastic solids and we want to know when we can expect exponential stability for our system. The model considered has been treated by Ies ßan and Quintanilla (2007), Ies ßan and Nappa (2008) and Alves et al (2009b). In what follows, we briefly describe this model.…”

Stability of non-classical thermoelasticity mixture problems

“…Limit cases σ = 0 and σ = 1, the heat flux law coincides with the fully parabolic Fourier law and the fully hyperbolic Gurtin-Pipkin law, respectively. In this direction, we quote the works of Alves et al [3,4,5] and Muñoz Rivera et al [21]. Reference [3] studies the problem (1.4)-(1.6) with classical theory of thermoelasticity (σ = 1) and under suitable assumptions on the constitutive coefficients (α, a ij , β i , ρ i ), the authors establish both exponential and polynomial decay rates for the corresponding solution.…”

“…Reference [3] studies the problem (1.4)-(1.6) with classical theory of thermoelasticity (σ = 1) and under suitable assumptions on the constitutive coefficients (α, a ij , β i , ρ i ), the authors establish both exponential and polynomial decay rates for the corresponding solution. In [4,5], the authors analyzed the problem (1.4)-(1.6) for Kelvin-Voigt materials with σ = 1. The first establishes decay rates for the solution and the second establishes the analyticity property of the corresponding semigroup.…”

On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

“…The author proved the slow decay of the solutions with respect to the time for elastic-porous materials when the only dissipation mechanism is the porous dissipation. After that, a lot of works were intended to clarify the behavior of the solutions (exponential decay, slow decay, impossibility of localization and/or analyticity) for solids with voids [4,5,9,10,13,14,16,17,18,20,19,21,23,24,29], for non-simple materials [8,25] or for mixtures of elastic solids [1,2,3,27,28]. Nevertheless, any attention has been paid up to now to micropolar elastic solids.…”