Uniqueness, continuous dependence, and spatial behavior of the solution in linear porous thermoelasticity with two relaxation times

On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity

“…In analogy with [26] and only for convenience related to possible future comparisons, we define Γ i (x, t) = − Ω i (x, t), and again we underline that the term ∂β i /∂t that flows from the expression (30) of ∂β * i /∂t does not have a suitable counterpart in the LHS of Equation (32). An integration by parts is then necessary:…”

“…We premise that our reference will be the work of Ieşan [30] in order to take into account the presence of pores into the thermoelastic matrix (similarly to [26,27]). Our study is framed into a fixed Cartesian system of axes Ox 1 x 2 x 3 , and the common summation and differentiation conventions are used.…”

“…The present work has to be considered as the natural continuation of the path recently traced in [26,27], where porous material matrices were investigated when coupled with heat transfer phenomena modeled through time-differential constitutive laws with two relaxation times. This was done not only in terms of well-posedness of the theory, but also obtaining interesting information about the influence of the voids on the model's response to certain external stimulations.…”

“…The attention paid to the knowledge of mechanical and thermal properties of porous materials is still very high (see e.g., [32,33]). Anyway, for a more detailed discussion about the possible applications of elastic and thermoelastic media with voids and the related growing interest in physical properties of such materials, we refer the reader to the Introduction of [26]. Going into the detail of the model studied, we remember that in [34] the authors prove uniqueness and continuous dependence of the solution for a linear thermoelastic model without voids under three-phase lag hypotheses while, substantially in parallel and in addition to other results, they define in [35] the restrictions under which its thermodynamic consistency is guaranteed.…”

“…Finally, some concluding remarks are given. We emphasize that in [26] something similar has been done taking into account only two relaxation times; differently, in this case, two different approaches aimed at verifying the uniqueness of the solution are proposed besides the proof of a continuous dependence theorem.…”