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Spectral analysis of hyperbolic Volterra integro-differential equations

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Abstract

Volterra integro-differential equations with unbounded operator coefficients in a Hilbert space are studied. The equations under consideration are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as integro-differential partial differential equations arising in the theory of viscoelasticity (see [4, 6]) and as the Gurtin–Pipkin integro-differential equations (see [1, 6]), which describe the process of heat propagation in media with memory at finite rate; these equations arise also in problems of averaging in multiphase media (Darcy’s law) (see [9]).

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    V. V. Vlasov & N. A. Rautian

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  1. V. V. Vlasov
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  2. N. A. Rautian
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Correspondence to V. V. Vlasov.

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Original Russian Text © V.V. Vlasov, N.A. Rautian, 2015, published in Doklady Akademii Nauk, 2015, Vol. 464, No. 6, pp. 656–659.

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Vlasov, V.V., Rautian, N.A. Spectral analysis of hyperbolic Volterra integro-differential equations. Dokl. Math. 92, 590–593 (2015). https://doi.org/10.1134/S1064562415050324

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