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Contemporary Mathematics. Fundamental Directions
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Contemporary Mathematics. Fundamental Directions, 2006, Volume 17, Pages 88–109 (Mi cmfd59)  
This article is cited in 11 scientific papers (total in 11 papers)

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
Full-text PDF (343 kB) Citations (11)
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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.
English version:
Journal of Mathematical Sciences, 2008, Volume 149, Issue 6, Pages 1679–1700
DOI: https://doi.org/10.1007/s10958-008-0089-x
Bibliographic databases:
UDC: 517.95+517.958
Language: Russian
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
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\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://mathscinet.ams.org/mathscinet-getitem?mr=2336461}
\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40549124903}
Linking options:
  • https://www.mathnet.ru/eng/cmfd59
  • https://www.mathnet.ru/eng/cmfd/v17/p88
    • This publication is cited in the following 11 articles:
    1. 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  mathnet  crossref
    2. 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  mathnet  crossref
    3. Victor V. Vlasov, Nadezda A. Rautian, Operator Theory: Advances and Applications, 236, Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, 2014, 517  crossref
    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  mathnet  crossref  mathscinet
    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  mathnet  crossref  crossref  mathscinet  isi
    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  mathnet  crossref  zmath  elib
    7. A. A. Gavrikov, A. S. Shamaev, “Some problems in acoustics of emulsions”, J. Math. Sci. (N. Y.), 179:3 (2011), 415–436  mathnet  crossref  zmath  elib
    8. V. V. Shumilova, “Averaging of acoustic equation for partially perforated viscoelastic material with channels filled by a liquid”, Journal of Mathematical Sciences, 190:1 (2013), 194–208  mathnet  mathnet  crossref  scopus
    9. 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  mathnet  crossref  mathscinet
    10. 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  crossref  mathscinet  zmath  isi  elib  elib
    11. Vlasov V.V., Wu J., “Spectral analysis and solvability of abstract hyperbolic equations with aftereffect”, Differ. Equ., 45:4 (2009), 539–548  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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