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Contemporary Mathematics. Fundamental Directions, 2010, Volume 35, Pages 44–59 (Mi cmfd144)  
This article is cited in 19 scientific papers (total in 19 papers)

Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect

V. V. Vlasova, J. Wub, G. R. Kabirovaa

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Russia, Moscow
b York University, Toronto, Canada
Full-text PDF (213 kB) Citations (19)
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Abstract: We study functional differential equations with unbounded operator coefficients in Hilbert spaces such that the principal part of the equation is an abstract hyperbolic equation perturbed by terms with delay and terms containing Volterra integral operators. The well-posed solvability of initial boundary-value problems for the specified problems in weighted Sobolev spaces on the positive semi-axis is established. Our concern is spectra of operator-valued functions that are symbols of the specified equations in the autonomous case. In particular, the spectra of the Gurtin–Pipkin equation is studied, which is an integrodifferential equation modelling the heat propagation in media with memory.
English version:
Journal of Mathematical Sciences, 2010, Volume 170, Issue 3, Pages 388–404
DOI: https://doi.org/10.1007/s10958-010-0093-9
Bibliographic databases:
Document Type: Article
UDC: 517.951
Language: Russian
Citation: V. V. Vlasov, J. Wu, G. R. Kabirova, “Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, CMFD, 35, PFUR, M., 2010, 44–59; Journal of Mathematical Sciences, 170:3 (2010), 388–404
Citation in format AMSBIB
\Bibitem{VlaWuKab10}
\by V.~V.~Vlasov, J.~Wu, G.~R.~Kabirova
\paper Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~1
\serial CMFD
\yr 2010
\vol 35
\pages 44--59
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd144}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2752638}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 170
\issue 3
\pages 388--404
\crossref{https://doi.org/10.1007/s10958-010-0093-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957737151}
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