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Asymptotics of the Spectrum of an Integro-Differential Equation Arising in the Study of the Flutter of a Viscoelastic Plate

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Abstract

In the paper, the asymptotics for the spectrum of the symbol of the oscillation equation of a viscoelastic plate in a liquid or gas flow is studied using operator analysis methods. This equation is the Gurtin–Pipkin equation with a relatively compact perturbation. Using an operator analog of Rouche’s theorem, we explicitly define an asymptotic representation of nonreal points of the spectrum for the symbol of the equation.

DOI 10.1134/S1061920821020059

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Acknowledgments

The author expresses his deep gratitude to the participants of the scientific seminar “Functional-differential and integro-differential equations and their spectral analysis,” in particular to V.V. Vlasov and N.A. Rautian, for active support, statement of the problem, and valuable advice.

Funding

This work was supported by a grant from the scientific school of the Lomonosov Moscow State University “Mathematical analysis of complex systems” under the direction of V. A. Sadovnichii, as well as by the Foundation for the Development of Theoretical Physics and Mathematics “Basis.”

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    A. V. Davydov

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    A. V. Davydov

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  1. A. V. Davydov
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Correspondence to A. V. Davydov.

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Davydov, A.V. Asymptotics of the Spectrum of an Integro-Differential Equation Arising in the Study of the Flutter of a Viscoelastic Plate. Russ. J. Math. Phys. 28, 188–197 (2021). https://doi.org/10.1134/S1061920821020059

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