Well posedness and stability result of Lord–Shulman system with microtemperature effects: The case ξμ∗=μ02

In this study, we investigate the Lord–Shulman porous elastic system with dissipation caused by the microtemperature effects. Here, the thermal conduction has a single‐phase‐lag that acts as a relaxation time and the energy associated with the solution is not required to be positive definite ξμ∗=μ02$$ \left(\xi {\mu}^{\ast }={\mu}_0^2\right) $$. We introduce a stability number χ$$ \chi $$ and prove using the multiplier technique that the exponential decay of the system is valid if χ=0$$ \chi =0 $$. Otherwise, we show that the system decays polynomially.