A thermoelastic problem with diffusion, microtemperatures, and microconcentrations

Dual-phase-lag one-dimensional thermo-porous-elasticity with microtemperatures

“…It is worth recalling that this theory has received a lots of attention in the past years (Feng and Apalara 2019;Feng and Yin 2019;Leseduarte et al 2010;Quintanilla 2006, 2007;Quintanilla 2019, 2020;Pamplona et al 2011;Santos et al 2017) to understand the relevance of the microstructural component in the whole material. In fact, the microstructure has deserved much attention and one of its possible components is the microtemperature (Bazarra et al 2019;Casas and Quintanilla 2005;Feng et al 2020;Grot 1969;Ieşan 2007;Ieşan and Quintanilla 2000;Passarella et al 2017;Riha 1975Riha , 1976.…”

Numerical analysis of a dual-phase-lag model with microtemperatures

“…where we have assumed that the reference temperature is uniformly equal to one in order to simplify the calculations, and vector Q i is the microheat flux average, q ij is the first moment heat flux tensor, η is the entropy and ε i is the first moment of the energy vector. The number of publications dealing with the study of elastic materials with microtemperatures is really huge (see, for instance [3,5,6,9,12,13,21,25,26,29,35]).…”

Spatial behaviour of thermoelasticity with microtemperatures and microconcentrations

“…We consider a thermoelastic material with microtemperatures and microconcentrations, as in [1], [2]. The mathematical model is represented by a system of partial differential equations with the coupling of the displacement, temperature, chemical potential, microconcentrations and microtemperatures fields.…”

“…Moreover, the asymptotic behaviour of the solution was discussed. In the isotropic case, the problem was analysed from a numerical point of view in [2] by means of the finite element method and the implicit Euler scheme.…”