Well-Posedness and Stability Results for a Nonlinear Damped Porous–Elastic System with Infinite Memory and Distributed Delay Terms

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation.