Abstract
In this paper, we consider the mixed initial boundary value problem in the context of a thermoelastic porous body having a dipolar structure. We intend to analyze the rate of decay of solutions to this problem to ensure that in a finite time, they become null. In our main result, we find that the combined contribution of the dipolar constitution of the body together with voids dissipation and thermal behavior cannot cause vanishing of the deformations in a finite time.
Highlights
We must outline that our study is dedicated to the dipolar structure for a porous thermoelastic body
This paper is dedicated to the linear mixed initial-boundary value problem in the context of the theory of thermoelasticity for bodies with voids that have a dipolar structure
We approach the question of the possibility of locating in time of solution for this problem, namely, we have shown that it is impossible to locate in a finite time of the solution of mixed problem
Summary
We must outline that our study is dedicated to the dipolar structure for a porous thermoelastic body. The unanimous opinion of the specialists is that the porous media with a dipolar structure very accurately shapes the structure and behavior of the bones of humans and, obviously, of animals This kind of material is an integral part of a more general theory, namely the microstructure, whose initiator was Eringen (see, for instance, [1,2]). Other studies of Quintanilla solve some questions regarding the location in time considering the solutions for problems back in time even in the case of theory of thermoelastic bodies with voids and of the theory of Green and Naghdi for thermoelasticity [26,27]. We should point out that our idea to consider the problem of localization in a finite time of solutions in the case of the theory of dipolar bodies with voids was inspired by the paper [32] of Quintanilla and Straughan. We prove that is not possible to locate a finite time for vanishing of the deformations
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