Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 668–672 | Cite as

Spectral Analysis of Linear Models of Viscoelasticity

  • V. V. Vlasov
  • N. A. Rautian


In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity (see [2, 5]), as Gurtin–Pipkin integrodifferential equations (see [1, 7]) that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law.

Keywords and phrases

integrodifferential equation spectral analysis operator-valued function 

AMS Subject Classification

34D05 34C23 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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