Abstract
We consider an operator semigroup arising in the study of an integro-differential equation modeling small transverse vibrations of a viscoelastic pipeline with allowance for Kelvin–Voigt damping. The explicit form of the generator of this semigroup is established, its spectrum is studied, and the norm of its resolvent is estimated. Based on these results, the analyticity of this semigroup is proved with the use of well-known facts from the theory of semigroups.
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ACKNOWLEDGMENTS
The author is grateful to Prof. V.V. Vlasov for posing this problem and for constant interest in the research as well as to all participants of the seminar headed by V.V. Vlasov for helpful advice, discussions, and guidance.
Funding
This work was supported by the Center for Fundamental and Applied Mathematics at Lomonosov Moscow State University.
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Translated by V. Potapchouck
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Tikhonov, Y.A. Analyticity of an Operator Semigroup Arising in Viscoelasticity Problems. Diff Equat 56, 797–812 (2020). https://doi.org/10.1134/S0012266120060129
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DOI: https://doi.org/10.1134/S0012266120060129