Uniqueness and stability in triple porosity thermoelasticity

Abstract

A general model for a triple porosity thermoelastic solid is presented in the linear anisotropic case. This allows for cross coupling of inertia coefficients, and cross coupling of interaction coefficients representing actions between pressures in the macro, meso and micro structures. Sufficient conditions are derived to demonstrate uniqueness and stability when the elastic coefficients are, in a precise sense, positive. Uniqueness is further demonstrated in the dynamical problem when the elastic coefficients are not sign-definite and possess only the major symmetry. An indication is given as to how one would proceed to obtain continuous dependence upon the inital data in the Hölder sense. The proof of uniqueness in the indefinite elasticity tensor case involves a logarithmic convexity method which proceeds by a novel choice of functional.