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 CMFD, 2006, Volume 17, Pages 88–109 (Mi cmfd59)

Spectral properties of some problems in mechanics of strongly inhomogeneous media

D. A. Kosmodem'yanskiia, A. S. Shamaevb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: 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.

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English version:
Journal of Mathematical Sciences, 2008, 149:6, 1679–1700

Bibliographic databases:

UDC: 517.95+517.958

Citation: D. A. Kosmodem'yanskii, A. S. Shamaev, “Spectral properties of some problems in mechanics of strongly inhomogeneous media”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, CMFD, 17, PFUR, M., 2006, 88–109; Journal of Mathematical Sciences, 149:6 (2008), 1679–1700

Citation in format AMSBIB
\Bibitem{KosSha06} \by D.~A.~Kosmodem'yanskii, A.~S.~Shamaev \paper Spectral properties of some problems in mechanics of strongly inhomogeneous media \inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~3 \serial CMFD \yr 2006 \vol 17 \pages 88--109 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd59} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336461} \elib{http://elibrary.ru/item.asp?id=13575052} \transl \jour Journal of Mathematical Sciences \yr 2008 \vol 149 \issue 6 \pages 1679--1700 \crossref{https://doi.org/10.1007/s10958-008-0089-x} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40549124903} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Vlasov V.V., Wu J., “Spectral analysis and solvability of abstract hyperbolic equations with aftereffect”, Differ. Equ., 45:4 (2009), 539–548
2. V. V. Vlasov, J. Wu, G. R. Kabirova, “Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect”, Journal of Mathematical Sciences, 170:3 (2010), 388–404
3. Vlasov V.V., Rautian N.A., Shamaev A.S., “Solvability and Spectral Analysis of Integro-Differential Equations Arising in the Theory of Heat Transfer and Acoustics”, Dokl. Math., 82:2 (2010), 684–687
4. V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics”, Journal of Mathematical Sciences, 190:1 (2013), 34–65
5. N. A. Rautian, “On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics”, Math. Notes, 90:3 (2011), 455–459
6. V. V. Vlasov, N. A. Rautian, “Well-defined solvability and spectral analysis of abstract hyperbolic integrodifferential equations”, J. Math. Sci. (N. Y.), 179:3 (2011), 390–414
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8. D. A. Zakora, “Operator approach to the ilyushin model for a viscoelastic body of parabolic type”, Journal of Mathematical Sciences, 225:2 (2017), 345–381
9. I. V. Romanov, A. S. Shamaev, “Some problems of distributed and boundary control for systems with integral aftereffect”, J. Math. Sci. (N. Y.), 234:4 (2018), 470–484
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