On the exponential decay of vibrations of damped elastic media
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 $\Omega$ tends to zero in the metric of $L_2(\Omega)$ exponentially with time.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 11, pp 1641-1659.
Citation Example: Goncharenko M. V., Khruslov E. Ya. On the exponential decay of vibrations of damped elastic media // Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1443-1459.