A domain of influence theorem for a natural stress–heat-flux problem in the Moore–Gibson–Thompson thermoelasticity theory

Jangid, Komal; Mukhopadhyay, Santwana

doi:10.1007/s00707-020-02833-1

Cited by 25 publications

(7 citation statements)

References 28 publications

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“…Domain of influence theorems under the type-II thermoelasticity theory are reported by Kumari and Mukhopadhyay [40, 41]. The domain of influence results for a natural stress–heat-flux problem under the MGT thermoelasticity theory have been recently discussed by Jangid and Mukhopadhyay [42].…”

Section: Introductionmentioning

confidence: 99%

A domain of influence theorem under MGT thermoelasticity theory

Jangid

Mukhopadhyay

2020

Mathematics and Mechanics of Solids

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The purpose of this article is to discuss domain of influence results under the Moore–Gibson–Thompson (MGT) thermoelasticity theory. We employ a mixed initial–boundary value problem concerning a homogeneous and isotropic material in view of the MGT thermoelasticity theory and establish the domain of influence theorem for potential–temperature disturbance. This theorem implies that the coupling of potential and temperature generates a thermoelastic disturbance, which vanishes outside the bounded domain for a prescribed bounded support of thermomechanical loading and for a finite time. The resulted bounded domain is subjected to the support of the prescribed load. The finite propagation of thermoelastic disturbance is also analyzed under the MGT theory, where the propagation speed depends on the parameters of the thermoelastic material. It is further shown that the domain of influence result for the present context reduces to the domain of influence result derived in the generalized thermoelasticity theory of Lord and Shulman under some conditions.

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Section: Introductionmentioning

confidence: 99%

A domain of influence theorem under MGT thermoelasticity theory

Jangid

Mukhopadhyay

2020

Mathematics and Mechanics of Solids

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“…It is worth noting that we can also obtain the MGT system of thermoelasticity as a particular case of the theory proposed by Gurtin [15], as can be seen in [16,17]. It is also worth remarking that this thermoelastic theory has received much attention in the last 2 years (see [9,[16][17][18][19][20][21][22][23][24][25][26][27], among others).…”

Section: Introductionmentioning

confidence: 73%

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

Bazarra

Quintanilla

2021

Mathematics and Mechanics of Solids

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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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A domain of influence theorem for a natural stress–heat-flux problem in the Moore–Gibson–Thompson thermoelasticity theory

Cited by 25 publications

References 28 publications

A domain of influence theorem under MGT thermoelasticity theory

A domain of influence theorem under MGT thermoelasticity theory

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

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

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