Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

This paper is concerned with the initial-boundary value problem for a log-arithmic Lamé system with a time delay in a bounded domain. We provethe well-posedness of the system by utilizing the semigroup theory. Then,we prove the existence of global solutions by using the well-depth method.In addition, we establish an exponential stability decay result under appro-priate assumptions on the weight of the time delay and that of frictional damping.