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Differential Equations

, Volume 55, Issue 4, pp 561–574 | Cite as

Well-Posed Solvability and the Representation of Solutions of Integro-Differential Equations Arising in Viscoelasticity

  • V. V. VlasovEmail author
  • N. A. RautianEmail author
Integral Equations
  • 1 Downloads

Abstract

For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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