On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

Magaña, Antonio; Quintanilla, R.

doi:10.1016/j.jmaa.2013.10.026

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…One of the important questions to be answered for any model is the decay rate of the solutions of the proposed system of equations when certain dissipation mechanisms are taken into account. Without trying to be exhaustive, let us refer to some studies of this kind carried out for porous materials , for mixtures of solids , or for micropolar materials . Through the paper, to simplify, we speak about slow decay or exponential decay of the solutions.…”

Section: Introduction and Basic Equationsmentioning

confidence: 99%

Exponential decay in nonsimple thermoelasticity of type III

Magaña

Quintanilla

2015

Math Methods in App Sciences

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Section: Introduction and Basic Equationsmentioning

confidence: 99%

Exponential decay in nonsimple thermoelasticity of type III

Magaña

Quintanilla

2015

Math Methods in App Sciences

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“…Starting from the assumption that for a thermally conducting Kelvin-Voigt solid subject to small strain and small temperature changes [23,38], we have…”

Section: Mathematical Modelmentioning

confidence: 99%

“…When τ ε → 0 , the Hookean response is recovered, i.e., σ = Eε. The Kelvin-Voigt thermoelasticity has been considered in a variety of viscoelastic applications, e.g., unbounded thermoviscoelastic domain with spherical cavity [35], vibration of an Euler Bernoulli beam [36,37], and micropolar thermoelasticity [38], and has been extended to the second-gradient media [39].…”

Section: Introductionmentioning

confidence: 99%

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

et al. 2023

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The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heating on a “nanoscale” plate is considered. The focus is on the anomalous heat transfer mechanisms that result from anomalous diffusion of hot electrons and are characterized by retarded thermal conduction, accelerated thermal conduction, or transition from super-thermal conductivity in the short-time response to sub-thermal conductivity in the long-time response and described by the fractional Jeffreys equation with three fractional parameters. The recent double-strip problem, Awad et al., Eur. Phy. J. Plus 2022, allowing the overlap between two propagating thermal waves, is generalized from the semi-infinite heat conductor case to thermoelastic case in the finite domain. The elastic response in the material is not simultaneous (i.e., not Hookean), rather it is assumed to be of the Kelvin–Voigt type, i.e., σ=Eε+τεε˙, where σ refers to the stress, ε is the strain, E is the Young modulus, and τε refers to the strain relaxation time. The delayed strain response of the Kelvin–Voigt model eliminates the discontinuity of stresses, a hallmark of the Hookean solid. The immobilization of thermal conduction described by the ordinary Jeffreys equation of heat conduction is salient in metals when the heat flux precedence is considered. The absence of the finite speed thermal waves in the Kelvin–Voigt model results in a smooth stress surface during the heating process. The temperature contours and the displacement vector chart show that the anomalous heat transfer characterized by retardation or crossover from super- to sub-thermal conduction may disrupt the ultrafast laser heating of metals.

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“…In several situations, the decay is not so fast and we will prove the polynomial decay for these situations. It is worth recalling that studying the rate of decay of the solutions for several non-classical theories has been the goal of many articles in this last decade [18,[22][23][24]. Thus, the present paper aims to be a new contribution in this line.…”

Section: Introductionmentioning

confidence: 99%

Decay of solutions for a mixture of thermoelastic solids with different temperatures

Rivera

Naso

Quintanilla³

2016

Computers & Mathematics with Applications

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Abstract. We study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures, that is, when each component of the mixture has its own temperature. In particular, we investigate the asymptotic behavior of the related solutions. We prove the exponential stability of solutions for a generic class of materials. In case of the coupling matrix B being singular, we find that in general the corresponding semigroup is not exponentially stable. In this case we obtain that the corresponding solution decays polynomially as t −1/2 in case of Neumann boundary condition. Additionally, we show that the rate of decay is optimal. For Dirichlet boundary condition, we prove that the rate of decay is t −1/6 . Finally, we demonstrate the impossibility of time-localization of solutions in case that two coefficients (related with the thermal conductivity constants) agree.

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On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

Cited by 9 publications

References 25 publications

Exponential decay in nonsimple thermoelasticity of type III

Exponential decay in nonsimple thermoelasticity of type III

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

Decay of solutions for a mixture of thermoelastic solids with different temperatures

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