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CMFD, 2015, Volume 58, Pages 22–42 (Mi cmfd277)  

This article is cited in 3 scientific papers (total in 3 papers)

Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory

V. V. Vlasov, N. A. Rautian

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: We study the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces and provide a spectral analysis of operator functions that are symbols of the specified equations. These equations represent an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory and other important applications. For the said integrodifferential equations, we obtain well-posedness results in weighted Sobolev spaces of vector functions defined on the positive semiaxis and valued in a Hilbert space. For the symbols of the said equations, we find the localization and the structure of the spectrum.

Funding Agency Grant Number
Russian Science Foundation 14-11-00754


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English version:
Journal of Mathematical Sciences, 2018, 233:4, 555–577

UDC: 517.929

Citation: V. V. Vlasov, N. A. Rautian, “Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory”, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, CMFD, 58, PFUR, M., 2015, 22–42; Journal of Mathematical Sciences, 233:4 (2018), 555–577

Citation in format AMSBIB
\Bibitem{VlaRau15}
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory
\inbook Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22--29, 2014). Part~1
\serial CMFD
\yr 2015
\vol 58
\pages 22--42
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd277}
\transl
\jour Journal of Mathematical Sciences
\yr 2018
\vol 233
\issue 4
\pages 555--577
\crossref{https://doi.org/10.1007/s10958-018-3943-5}


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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. D. A. Zakora, “Exponential Stability of a Certain Semigroup and Applications”, Math. Notes, 103:5 (2018), 745–760  mathnet  crossref  crossref  isi  elib
    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
  • Современная математика. Фундаментальные направления
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