Well-posedness and exponential decay for a porous-thermoelastic system with second sound and a distributed delay term

Abstract

In this paper, we consider one-dimensional linear porous-thermoelastic system with distributed delay acting on the displacement equation.Under suitable assumptions on the weight of distributed delay and the wave speeds, we first prove the well-posedness of the system by using the semigroup theory. Also, we establish the exponential stability of the solution by introducing an appropriate Lyapunov functional. For the case of equal speeds of wave propagation.