Moore–Gibson–Thompson thermoelasticity

Abstract

We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parameter in the Green–Naghdi type III model. We analyse the one- and three-dimensional cases. In three dimensions, we obtain the well-posedness and the stability of solutions. In one dimension, we obtain the exponential decay and the instability of the solutions depending on the conditions over the system of constitutive parameters. We also propose possible extensions for these theories.

Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature

“…Along the same lines of [44], we now propose a thermoelasticity model, where heat conduction is ruled by the MGT law (2.4). Actually, in more generality, we consider a kernel g ij of which (2.4) is only a particular case, and whose properties will be specified shortly.…”

“…The goal of the present paper is to develop a thermoelastic theory based on heat conduction of MGT type. This strategy has been first devised in [44]. However, we will consider here, rather than the pure MGT, an integro-differential equation of which the MGT heat law (1.6) is just a particular instance, corresponding to the choice of a (negative) exponential convolution kernel.…”

“…When τ is independent of x, equation (2.6) can be rewritten in a generalized MGT form. Indeed, adding (2.6) and its time-derivative times τ , and keeping in mind the explicit form of g ij given by (2.3), we obtain (see [44])…”

Thermoelastic Processes by a Continuous Heat Source Line in an Infinite Solid via Moore–Gibson–Thompson Thermoelasticity

“…This theory has been derived from a third-order differential equation, which has been incorporated into the meaning of some considerations of fluid dynamics [ 24 ]. A new thermoelastic model of heat conduction presented by the Moore–Gibson–Thompson equation has been constructed by Quintanilla [ 25 ]. The modified heat equation proposed by Quintanilla [ 25 ] has been achieved after applying the relaxation parameter in the Green–Naghdi Type III model.…”

“…A new thermoelastic model of heat conduction presented by the Moore–Gibson–Thompson equation has been constructed by Quintanilla [ 25 ]. The modified heat equation proposed by Quintanilla [ 25 ] has been achieved after applying the relaxation parameter in the Green–Naghdi Type III model. The number of papers devoted to this theory has grown significantly since the advent of Moore–Gibson–Thompson theory [ 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ].…”