Exponential stability of Lord Shulman thermoelastic system with porous damping and distributed delay term

Abstract

In this paper, we consider a one-dimensional Lord–Shulman thermoelastic system [C. Cattaneo, On a form of heat equation which eliminates the paradox of instantaneous propagation, C. R. Acad. Sci. Paris 247 (1958) 431–433] with porous damping and distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well posedness of the system by using semigroup theory and we show that the dissipations due to thermal effects with porous damping are strong enough to stabilise the system exponentially, independently of the wave speeds of the system.