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

DOI10.3103/S0027132222020073OpenAlexW4285103878MaRDI QIDQ2674662

Yu. A. Tikhonov

Publication date: 14 September 2022

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132222020073

zbMATH Keywords

resolventspectraabstract integro-differential equationoperator-function

Mathematics Subject Classification ID

Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34Kxx) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74Dxx) General theory of linear operators (47Axx)

Cites Work

• A new approach to equations with memory
• Spectral analysis of integrodifferential operators arising in the study of flutter of a viscoelastic plate
• Heat equation with memory: Lack of controllability to rest
• Instability spectrum of an operator bundle
• On an operator pencil arising in the problem of beam oscillation with internal damping
• Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory
• Analysis of operator models arising in problems of hereditary mechanics
• Study of Kelvin-Voigt models arising in viscoelasticity
• The controllability of the Gurtin-Pipkin equation: a cosine operator approach
• A general theory of heat conduction with finite wave speeds
• Asymptotic stability in viscoelasticity
• Well-Posedness and Spectral Analysis of Hyperbolic Volterra Equations of Convolution Type
• Thermodynamics of Materials with Memory
• Spectra of the Gurtin–Pipkin Type Equations
• Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels
• Properties of solutions of integro-differential equations arising in heat and mass transfer theory
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