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Well-Posedness and Spectral Analysis of Volterra Integro-Differential Equations with Singular Kernels

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Abstract

Integro-differential equations with unbounded operator coefficients in a Hilbert space are considered. Such equations arise in viscoelasticity theory, thermal physics, and homogenization problems in multiphase media. Initial–boundary value problems for the indicated equations are proved to be well posed, and their spectral analysis is performed.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    V. V. Vlasov & N. A. Rautian

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

Additional information

Original Russian Text © V.V. Vlasov, N.A. Rautian, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 6.

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Vlasov, V.V., Rautian, N.A. Well-Posedness and Spectral Analysis of Volterra Integro-Differential Equations with Singular Kernels. Dokl. Math. 98, 502–505 (2018). https://doi.org/10.1134/S1064562418060303

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  • DOI: https://doi.org/10.1134/S1064562418060303

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