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Contemporary Mathematics. Fundamental Directions, 2011, Volume 39, Pages 36–65 (Mi cmfd172)  
This article is cited in 32 scientific papers (total in 32 papers)

Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics

V. V. Vlasova, N. A. Rautianb, A. S. Shamaeva

a Moscow Lomonosov State University, Faculty of Mechanics and Mathematics, Moscow, Russia
b Russian Plekhanov Academy of Economics, Faculty of Economics and Mathematics, Moscow, Russia
Full-text PDF (325 kB) Citations (32)
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Abstract: In the present paper, we study integrodifferential equations with unbounded operator coefficients in Hilbert spaces. The principal part of the equation is an abstract hyperbolic equation perturbed by summands with Volterra integral operators. These equations represent an abstract form of the Gurtin–Pipkin integrodifferential equation describing the process of heat conduction in media with memory and the process of sound conduction in viscoelastic media and arise in averaging problems in perforated media (the Darcy law).
The correct solvability of initial-boundary problems for the specified equations is established in weighted Sobolev spaces on a positive semiaxis.
Spectral problems for operator-functions are analyzed. Such functions are symbols of these equations. The spectrum of the abstract integrodifferential Gurtin–Pipkin equation is investigated.
English version:
Journal of Mathematical Sciences, 2013, Volume 190, Issue 1, Pages 34–65
DOI: https://doi.org/10.1007/s10958-013-1245-5
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics”, Partial differential equations, CMFD, 39, PFUR, M., 2011, 36–65; Journal of Mathematical Sciences, 190:1 (2013), 34–65
Citation in format AMSBIB
\Bibitem{VlaRauSha11}
\by V.~V.~Vlasov, N.~A.~Rautian, A.~S.~Shamaev
\paper Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics
\inbook Partial differential equations
\serial CMFD
\yr 2011
\vol 39
\pages 36--65
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2830676}
\transl
\jour Journal of Mathematical Sciences
\yr 2013
\vol 190
\issue 1
\pages 34--65
\crossref{https://doi.org/10.1007/s10958-013-1245-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874950458}
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    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Современная математика. Фундаментальные направления
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