Polynomial stability for Lord–Shulman porous elasticity with microtemperature and strong time delay

Abstract

In this paper, we study a porous thermoelastic system with microtemperature and strong time delay acting on the volume fraction equation. The thermal effect of microtemperature is based on the Lord–Shulman theory (J Mech Phys Solids. 15(5) (1967), 299–309.), while the strong delay is motivated by Makheloufi's et al. recent work (Math Meth Appl Sci. 44 (2021), 6301–6317.). To prove the well‐posedness of the system, lack of exponential stability and the polynomial decay with optimal rate, we use the semigroup theory of linear operators.