Yu. A. Tikhonov, “On the spectrum localization of an operator-function arising at studying oscillations of a viscoelastic pipeline with Kelvin–Voigt friction”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, Number 2,Pages <nobr>23

Mathematics

On the spectrum localization of an operator-function arising at studying oscillations of a viscoelastic pipeline with Kelvin–Voigt friction

Yu. A. Tikhonov^ab

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Moscow Center for Fundamental and Applied Mathematics

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 spectra localization is determined in the paper and its resolvent norm is estimated in a domain free of spectral points.

Key words: abstract integro-differential equation, operator-function, spectra, resolvente.

UDC: 517.984.4

Received: 17.02.2021