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Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 2, Pages 219–243 (Mi mmo565)  

This article is cited in 6 scientific papers (total in 6 papers)

Properties of solutions of integro-differential equations arising in heat and mass transfer theory

V. V. Vlasov, N. A. Rautian

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The aim of the present paper is to study the asymptotic behavior of solutions of integro-differential equations on the basis of spectral analysis of their symbols. To this end, we obtain representations of strong solutions of these equations in the form of a sum of terms corresponding to the real and nonreal parts of the spectrum of the operator functions that are the symbols of these equations. These representations are new for the class of integro-differential equations considered in the paper.

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English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 185–204

UDC: 517.97
MSC: 47G20, 34K30, 47A56, 34K12
Received: 25.03.2014

Citation: V. V. Vlasov, N. A. Rautian, “Properties of solutions of integro-differential equations arising in heat and mass transfer theory”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 219–243; Trans. Moscow Math. Soc., 75 (2014), 185–204

Citation in format AMSBIB
\Bibitem{VlaRau14}
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Properties of solutions of integro-differential equations arising in heat and~mass transfer theory
\serial Tr. Mosk. Mat. Obs.
\yr 2014
\vol 75
\issue 2
\pages 219--243
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo565}
\elib{https://elibrary.ru/item.asp?id=23780164}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2014
\vol 75
\pages 185--204
\crossref{https://doi.org/10.1090/S0077-1554-2014-00231-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960129426}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Vlasov, N. A. Rautian, “Spektralnyi analiz integrodifferentsialnykh uravnenii v gilbertovom prostranstve”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 53–71  mathnet
    2. V. V. Vlasov, N. A. Rautian, “Well-posed solvability of Volterra integro-differential equations in Hilbert space”, Differ. Equ., 52:9 (2016), 1123–1132  crossref  mathscinet  zmath  isi  scopus
    3. V. V. Vlasov, N. A. Rautian, “Issledovanie operatornykh modelei, voznikayuschikh v teorii vyazkouprugosti”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 60–73  mathnet  crossref
    4. V. V. Vlasov, N. A. Rautian, “Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels”, Trans. Moscow Math. Soc., 80 (2019), 169–188  mathnet  crossref  elib
    5. V. V. Vlasov, N. A. Rautian, “Correct solvability and representation of solutions of Volterra integrodifferential equations with fractional exponential kernels”, Dokl. Math., 100:2, 467–471  crossref  crossref  zmath  isi  elib  scopus
    6. V. V. Vlasov, N. A. Rautian, “Well-posed solvability and the representation of solutions of integro-differential equations arising in viscoelasticity”, Differ. Equ., 55:4 (2019), 561–574  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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