Well-Posedness and Stability Results for An Integro-Differential Porous-Elastic System with Time Delay Term

This paper is concerned with the integro-differential porous-elastic system with delay term. Firstly, we establish the global existence and uniqueness results utilizing Faedo-Galerkin approximations along with some energy estimates. Later, by using energy method and by constructing a suitable Lyapunov functional, we prove an exponential decay result under some conditions. While the polynomial decay of solutions result is established by utilizing the second-order energy method. These results generalize and improve some earlier related results in the literature.