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

Abstract

Through the present work, we want to lay the foundation of the well-posedness question for a linear model of thermoelasticity here proposed, in which the presence of voids into the elastic matrix is taken into account following the Cowin-Nunziato theory, and whose thermal response obeys a three-phase lag time-differential heat transfer law. By virtue of the linearity of the model investigated, the basic initial-boundary value problem is conveniently modified into an auxiliary one; attention is paid to the uniqueness question, which is addressed through two alternative paths, i.e., the Lagrange identity and the logarithmic convexity methods, as well as to the continuous dependence issue. The results are achieved under very weak assumptions involving constitutive coefficients and delay times, at most coincident with those able to guarantee the thermodynamic consistency of the model.

Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

“…The present work complements, together with [1], the study of thermoelastic materials with voids and three delay times, providing a framework superimposable to the one described in [8] for media with a porous elastic matrix and only two delay times. The work plan is the following.…”

“…First of all, it is important to underline that this communication represents a natural extension of the study of well-posedness started in [1]; for this reason, the reading of the present paper should not ignore, and indeed should be strictly connected to, the contents of [1] also because-in order to avoid unnecessary duplications-we will not report here the equations underlying the mathematical model object of investigation, nor will we specify the conventions used, limiting ourselves to their citation. Furthermore, we immediately point out that, in the present investigation, the reference time-differential heat conduction law is assumed as follows:…”

“…• Two delay times with compact [7] and porous [8] elastic matrices; • Three delay times with compact [9] and porous [1] elastic matrices.…”

Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories

“…Othman and Abd-Elaziz [35] applied three thermoelastic theories considering the micro-temperatures and gravity influence on the porous thermoelastic medium. Carini and Zampoli [36] studied in detail the three-phase-lag theory in porous matrices assuming three delay times in linearity of thermoelasticity. Marin et al [37] discussed some results on the dipolar structure of bodies in the context of Green-Lindsay thermoelasticity.…”

The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux

“…Biswas [26] investigated surface waves in nonlocal, orthotropic thermoelastic porous media. Carini and Zampoli [27] studied porous matrices with three delay times. Abbas and Marin [28] presented the analytical solution of a two-dimensional generalized thermodiffusion problem subjected to a laser pulse.…”