Geodesic
Spectral properties of some problems in mechanics of strongly inhomogeneous media
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, Tome 17 (2006), pp. 88-109

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Spectral properties of the following three homogenized problems in mechanics of strongly inhomogeneous media are considered: the problem of “double porosity”, the problem of vibration of a mixture of two viscous compressible fluids, and the problem of vibration of a medium consisting of an elastic frame and a viscous fluid. Interesting results about the structure of spectra and the presence of so-called “spectral gaps” are obtained for each of these cases. 
@article{CMFD_2006_17_a6,
     author = {D. A. Kosmodem'yanskii and A. S. Shamaev},
     title = {Spectral properties of some problems in mechanics of strongly inhomogeneous media},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {88--109},
     publisher = {mathdoc},
     volume = {17},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_17_a6/}
}
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D. A. Kosmodem'yanskii; A. S. Shamaev. Spectral properties of some problems in mechanics of strongly inhomogeneous media. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, Tome 17 (2006), pp. 88-109. http://geodesic.mathdoc.fr/item/CMFD_2006_17_a6/