On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

Bazarra, Noelia; Quintanilla, R.

doi:10.1177/1081286521994258

Cited by 15 publications

(6 citation statements)

References 31 publications

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“…Later, some people (see, for instance, Muñoz Rivera 2 and Slemrod 3 ) proved the exponential decay for dimension one, and we cannot expect the exponential stability for a dimension greater than one (see Koch 4 and Lebeau and Zuazua 5 ). For other thermoelastic theories (see previous studies 6–9 ), it has been also proved the exponential decay in one dimension and for radial solutions in the multidimensional setting (see Bazarra et al 10 and Jiang et al 11 ).…”

Section: Introductionmentioning

confidence: 83%

On the thermoelasticity with several dissipative mechanisms of type III

Fernández

Quintanilla

2023

Math Methods in App Sciences

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Section: Introductionmentioning

confidence: 83%

On the thermoelasticity with several dissipative mechanisms of type III

Fernández

Quintanilla

2023

Math Methods in App Sciences

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“…Marin et al 32 used the thermoelasticity theory by applying some initial values to investigate the MGT model in a dipolar medium. Bazarra et al 33 studied exponential decay w.r.t. time variable for radially symmetric solutions in the context of MGT theory of thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Analysis of axisymmetric deformation in generalized micropolar thermoelasticity within the framework of Moore-Gibson-Thompson heat equation incorporating non-local and hyperbolic two-temperature effect

Kumar,

Kaushal,

Kochar

2024

The Journal of Strain Analysis for Engineering Design

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An axisymmetric problem in micropolar thermoelastic model based on the Moore-Gibson-Thompson heat equation (MGT) under non-local and hyperbolic two-temperature (HTT) is explored due to mechanical loading. After transforming the system of equations into dimensionless form and employing potential functions, a new set of governing equations are solved using Laplace and Hankel transforms. A specific set of restrictions are applied on the boundary in the form of ring load and disk load for examining the significance of the problem. The transformed form of components of displacement, stresses, tangential couple stress, conductive temperature, and thermodynamic temperature are obtained. A numerical inversion technique is applied to recover the physical quantities in the original domain. The graphic representation of numerical findings for stress components, tangential couple stress, and conductive temperature reveals the impact of non-local and HTT parameters. Certain cases of interest are drawn out. Physical views presented in the article may be useful for the composition of new materials, geophysics, earthquake engineering, and other scientific disciplines.

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“…On the other hand, in the last decade great interest has been developed to understand the so-called Moore-Gibson-Thompson equation which was first used in fluid mechanics. Recently, this equation has been considered as a heat equation (and then, to analyze the Moore-Gibson-Thompson thermoelasticity) [1][2][3]5,6,13,14,16,22,23,28,31] and a new kind of viscous elastic materials [12,13,27]. In this work, we want to consider a mixture of a viscous solid of Moore-Gibson-Thompson type and an elastic material.…”

Section: Introductionmentioning

confidence: 99%

On a mixture of an MGT viscous material and an elastic solid

Fernández

Quintanilla

2022

Acta Mech

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A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelastic type material and an elastic solid. To this end, we first derive the system of equations governing the deformations of such material. We give the suitable assumptions to obtain an existence and uniqueness result. The semigroups theory of linear operators is used. The paper concludes by proving the exponential decay of solutions with the help of a characterization of the exponentially stable semigroups of contractions and introducing an extra assumption. The impossibility of location is also shown.

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On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

Cited by 15 publications

References 31 publications

On the thermoelasticity with several dissipative mechanisms of type III

On the thermoelasticity with several dissipative mechanisms of type III

Analysis of axisymmetric deformation in generalized micropolar thermoelasticity within the framework of Moore-Gibson-Thompson heat equation incorporating non-local and hyperbolic two-temperature effect

On a mixture of an MGT viscous material and an elastic solid

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