Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement

Abstract

In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional.