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.