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.