A domain of influence theorem under MGT thermoelasticity theory

Abstract

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.

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

“…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).…”

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

“…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.…”

On the numerical approximation of a problem involving a mixture of a MGT viscous material and an elastic solid

“…Therefore, we can also consider a thermoelastic theory based on the Moore-Gibson-Thompson heat equation. In fact, many contributions have been published on this theory over the last two years (see [1][2][3]5,6,15,16,18,24,25,30,33] among others). At the same time, it has also been shown how to obtain a viscous effect for different materials [14,15,29] following the Moore-Gibson-Thompson proposition.…”