On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod
Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 369-383
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In this paper, we study the problem of the boundary accumulation of a discrete spectrum, which is essential for a boundary-value problem of fourth order arising in the theory of small transverse vibrations in an inhomogeneous viscoelastic rod (a Kelvin–Voigt body). We establish conditions for such an accumulation and its asymptotics, which are expressed in terms of the coefficients defining the problem posed by the differential expression. The results obtained are illustrated by numerical computation data.
@article{MZM_2006_79_3_a4,
author = {A. A. Vladimirov},
title = {On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod},
journal = {Matemati\v{c}eskie zametki},
pages = {369--383},
publisher = {mathdoc},
volume = {79},
number = {3},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/}
}
TY - JOUR AU - A. A. Vladimirov TI - On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod JO - Matematičeskie zametki PY - 2006 SP - 369 EP - 383 VL - 79 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/ LA - ru ID - MZM_2006_79_3_a4 ER -
%0 Journal Article %A A. A. Vladimirov %T On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod %J Matematičeskie zametki %D 2006 %P 369-383 %V 79 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/ %G ru %F MZM_2006_79_3_a4
A. A. Vladimirov. On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod. Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 369-383. http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/