A qualitative study for Moore–Gibson–Thompson theories with two temperatures

The aim of this paper is to obtain qualitative properties of the solutions to problems related to heat conduction of the Moore–Gibson–Thompson type with two temperatures and Zener viscoelasticity. In particular, uniqueness and instability results of solutions are obtained when we impose very relaxed conditions on the constitutive coefficients. We consider the case where the elasticity tensor is not necessarily positive definite. The fundamental tool to obtain our results is the logarithmic convexity method