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On the Spectrum Localization of an Operator-Function Arising at Studying Oscillations of a Viscoelastic Pipeline with Kelvin–Voigt Friction

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Abstract

In this paper we consider an operator function being a symbol of the abstract integro-differential equation describing the oscillations of a viscoelastic tube. The operator-function spectrum localization is determined in the paper and its resolvent norm is estimated in a domain free of spectral points.

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ACKNOWLEDGMENTS

The author is grateful to V.V. Vlasov for problem formulation and to all participants of the workshop under his guidance for fruitful remarks, discussions, and support in this work.

Funding

The study is supported by the Interdisciplinary Research and Educational School Mathematical Methods of Analysis of Complex Systems of the Lomonosov Moscow State University.

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Authors and Affiliations

  1. Chair of Mathematical Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    Yu. A. Tikhonov

  2. Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia

    Yu. A. Tikhonov

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  1. Yu. A. Tikhonov
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Correspondence to Yu. A. Tikhonov.

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Translated by E. Oborin

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Tikhonov, Y.A. On the Spectrum Localization of an Operator-Function Arising at Studying Oscillations of a Viscoelastic Pipeline with Kelvin–Voigt Friction. Moscow Univ. Math. Bull. 77, 73–85 (2022). https://doi.org/10.3103/S0027132222020073

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