On the exponential decay of vibrations of damped elastic media - Goncharenko, M. V.; Khruslov, E. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
We consider a homogenized system of equations that is a macroscopic model of nonstationary vibrations of an elastic medium with a large number of small cavities filled with viscous incompressible liquid (wet elastic medium). It is proved that the solution of the initial boundary-value problem for this system in a bounded domain $Ω$ tends to zero in the metric of $L_2(Ω)$ exponentially with time.