We consider a homogenized system of equations used as a macroscopic model of nonstationary vibrations of an elastic medium containing a large number of small cavities filled with viscous incompressible liquid (damped elastic medium). It is shown that the solution of the initial-boundary-value problem for this system in a bounded domain Ω approaches zero in the metric of L 2(Ω) as an exponential function of time.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1443–1459, November, 2011.
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Goncharenko, M.V., Khruslov, E.Y. On the exponential decay of vibrations of damped elastic media. Ukr Math J 63, 1641–1659 (2012). https://doi.org/10.1007/s11253-012-0604-6
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DOI: https://doi.org/10.1007/s11253-012-0604-6