Modeling triple porosity under local thermal non-equilibrium

Abstract

In this paper, we present a model describing the evolutionary behavior of materials with triple porosity under local thermal non-equilibrium. The constitutive equations are presented for anisotropic and inhomogeneous materials and so they take into account the terms representing connectivity between the pressures and temperatures in the various pore scales. Further, the basic initial boundary value problems are investigated by using the Lagrange identity and the logarithmic convexity methods. We introduce a functional representing an appropriate measure of the solution to the initial boundary value problem for the model in concern and by means of the Lagrange identity method we are able to establish a uniqueness result. We also establish some estimates describing the continuous data dependence of solution with respect to the initial data and with respect to the various supply terms. Finally, we show how the above functional can be used in combination with the logarithmic convexity method in order to prove again that the solution is unique.