A non‐homogeneous weakly damped Lamé system with time‐dependent delay

Abstract

This paper is concerned with asymptotic stability of the Lamé 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.