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Journal of Mathematical Sciences

, Volume 190, Issue 1, pp 34–65 | Cite as

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

  • V. V. Vlasov
  • N. A. Rautian
  • A. S. Shamaev
Article

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.

Keywords

Hardy Space Asymptotic Representation Laplace Transformation Real Zero Unbounded Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Moscow Lomonosov State University, Faculty of Mechanics and MathematicsMoscowRussia
  2. 2.Russian Plekhanov Academy of Economics Faculty of Economics and MathematicsMoscowRussia

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