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Contemporary Mathematics. Fundamental Directions, 2015, Volume 58, Pages 22–42 (Mi cmfd277)  

This article is cited in 25 scientific papers (total in 25 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
References:
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
English version:
Journal of Mathematical Sciences, 2018, Volume 233, Issue 4, Pages 555–577
DOI: https://doi.org/10.1007/s10958-018-3943-5
Document Type: Article
UDC: 517.929
Language: Russian
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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  • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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