Ukrainian Mathematical Journal

, Volume 63, Issue 11, pp 1641–1659 | Cite as

On the exponential decay of vibrations of damped elastic media

  • M. V. Goncharenko
  • E. Ya. Khruslov

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.


Exponential Decay Vector Function Bilinear Form Elastic Medium Elasticity Tensor 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • M. V. Goncharenko
    • 1
  • E. Ya. Khruslov
    • 1
  1. 1.KharkovUkraine

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