A non-homogeneous weakly damped Lame system with time-dependent delay

This paper is concerned with asymptotic stability of the Lame system, which arises in isotropic elasticity and has remarkable application in seismology. The main feature is the well-posedness and the energy decay when a time-dependent delay competes with a frictional damping. Following recent literature for systems with time-varying delay, our problem is written as a Cauchy problem with time-dependent operators and apply the so called Kato's CD-system method. To this regard, we present a simple argument for the needed stability to a family of time-dependent semigroup generators.