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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 24–28 (Mi into158)  
This article is cited in 5 scientific papers (total in 5 papers)

Ûpectral analysis of linear models of viscoelasticity

V. V. Vlasov, N. A. Rautian

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (282 kB) Citations (5)
Abstract: In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity, as Gurtin–Pipkin integrodifferential equations that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law).
Keywords: integrodifferential equation, spectral analysis, operator-valued function.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00349_à
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 668–672
DOI: https://doi.org/10.1007/s10958-018-3766-4
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34D05, 34C23
Language: Russian
Citation: V. V. Vlasov, N. A. Rautian, “Ûpectral analysis of linear models of viscoelasticity”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 24–28; J. Math. Sci. (N. Y.), 230:5 (2018), 668–672
Citation in format AMSBIB
\Bibitem{VlaRau17}
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Ûpectral analysis of linear models of viscoelasticity
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 24--28
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into158}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801378}
\zmath{https://zbmath.org/?q=an:1394.45013}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 668--672
\crossref{https://doi.org/10.1007/s10958-018-3766-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044471635}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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