On porous‐elastic system with a time‐varying delay term in the internal feedbacks

Abstract

In this article, we consider the one‐dimensional equations of an homogeneous and isotropic porous‐elastic solid with interior time‐dependent delay term feedbacks. First, using the variable norm technique of T. Kato, we prove that the system is well‐posed under some hypothesis adopted. Then, via a suitable Lyapunov functional, we show that the system is exponentially stable.