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CMFD, 2010, Volume 35, Pages 44–59 (Mi cmfd144)  

This article is cited in 10 scientific papers (total in 10 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

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.

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English version:
Journal of Mathematical Sciences, 2010, 170:3, 388–404

Bibliographic databases:

UDC: 517.951

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{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957737151}


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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. Vlasov V.V., Rautian N.A., Shamaev A.S., “Solvability and spectral analysis of integro-differential equations arising in the theory of heat transfer and acoustics”, Dokl. Math., 82:2 (2010), 684–687  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics”, Journal of Mathematical Sciences, 190:1 (2013), 34–65  mathnet  crossref  mathscinet
    3. N. A. Rautian, “On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics”, Math. Notes, 90:3 (2011), 455–459  mathnet  crossref  crossref  mathscinet  isi
    4. V. V. Vlasov, N. A. Rautian, “Well-defined solvability and spectral analysis of abstract hyperbolic integrodifferential equations”, J. Math. Sci. (N. Y.), 179:3 (2011), 390–414  mathnet  crossref  zmath  elib
    5. A. A. Gavrikov, A. S. Shamaev, “Some problems in acoustics of emulsions”, J. Math. Sci. (N. Y.), 179:3 (2011), 415–436  mathnet  crossref  zmath  elib
    6. A. S. Shamaev, V. V. Shumilova, “O spektre odnomernykh kolebanii sloistogo kompozita s komponentami iz uprugogo i vyazkouprugogo materialov”, Sib. zhurn. industr. matem., 15:4 (2012), 124–134  mathnet
    7. Shamaev A.S., Shumilova V.V., “The Spectrum of Natural Vibrations in a Medium Composed of Layers of Elastic Material and Viscous Fluid”, Dokl. Phys., 58:1 (2013), 33–36  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
    8. V. V. Vlasov, N. A. Rautian, “Properties of solutions of integro-differential equations arising in heat and mass transfer theory”, Trans. Moscow Math. Soc., 75 (2014), 185–204  mathnet  crossref  elib
    9. V. V. Vlasov, N. A. Rautian, “Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory”, Journal of Mathematical Sciences, 233:4 (2018), 555–577  mathnet  crossref
    10. 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
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