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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 11, Pages 1829–1843 (Mi zvmmf10855)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectral analysis of a viscoelasticity problem

D. A. Zakoraab

a Voronezh State University, Voronezh, Russia
b Vernadsky Crimean Federal University, Simferopol, Russia

Abstract: An eigenvalue problem associated with small movements of a viscoelastic body fixed on the boundary of a bounded domain is studied. The spectrum of the problem is proved to lie in a vertical strip bounded away from the imaginary axis and to be symmetric about the real axis. The essential spectrum of the problem consists of a finite number of points on the real axis. There are two sequences of complex conjugate eigenvalues condensing toward infinity. Under certain additional conditions, the spectrum that does not lie on the real axis is bounded away from it.

Key words: viscoelastic body, integro-differential equation, spectrum, essential spectrum, asymptotic behavior of eigenvalues.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037


DOI: https://doi.org/10.31857/S004446690003536-0

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:11, 1761–1774

Bibliographic databases:

UDC: 517.955
Received: 08.12.2017
Revised: 16.01.2018

Citation: D. A. Zakora, “Spectral analysis of a viscoelasticity problem”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1829–1843; Comput. Math. Math. Phys., 58:11 (2018), 1761–1774

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. O. Tsvetkov, “Zadacha o normalnykh kolebaniyakh vyazkoi stratifitsirovannoi zhidkosti s uprugoi membranoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:2 (2021), 311–330  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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