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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 11, Pages 1829–1843
DOI: https://doi.org/10.31857/S004446690003536-0 (Mi zvmmf10855) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Spectral analysis of a viscoelasticity problem

D. A. Zakoraab

a Voronezh State University, Voronezh, Russia
b Vernadsky Crimean Federal University, Simferopol, Russia
Citations (3)
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DOI: https://doi.org/10.31857/S004446690003536-0
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
Received: 08.12.2017
Revised: 16.01.2018
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 11, Pages 1761–1774
DOI: https://doi.org/10.1134/S0965542518110179
Bibliographic databases:
Document Type: Article
UDC: 517.955
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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