Stability signatures for porous thermoelasticity with microtemperature and without temperature

In this paper, we provide necessary and sufficient conditions for obtaining the stabilization properties for the one-dimensional Lord-Shulman thermoelastic theory with porosity subject to microtemperature but without temperature where the microtemperature conduction equations are governed by Cattaneo-Maxwell's law. Based on recent results due to Bazarra et al., we introduce a stability number ?(0) involving all coefficients of the system, and we prove that the exponential decay of the corresponding semigroup holds if and only if ?(0) = 0 . Otherwise, we show that the system loses exponential stability and its solution decays polynomially with a rate equal to 1 /vt .