On the decay of a porous thermoelasticity type III with constant delay

This paper focuses on the well-posedness and asymptotic stability of solutions of a delayed porous thermoelastic system of type III, where the delay acts on the heat equation. We investigate the cases of equal and non-equal wave speeds. In the first case, we establish an exponential rate of decay provided that the weight of the delay is strictly less than the weight of the thermal dissipation. In the case of non-equal wave speeds, we obtain a polynomial decay rate.