Operator approach to the Ilyushin model for a viscoelastic body of parabolic type

DOI10.1007/s10958-017-3473-6zbMath1379.35311OpenAlexW2739364683MaRDI QIDQ1683197

Dmitriĭ A. Zakora

Publication date: 6 December 2017

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-017-3473-6

zbMATH Keywords

viscoelastic bodyasymptotic formula for the series of eigenvaluesIlyushin modelsecond-order integrodifferential equation

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items

On small motions of hydrodynamic systems containing a viscoelastic fluid

Cites Work

• Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics
• The operator approach to Il'yushin's models of viscoelastic media under the isothermal processes of deformation
• Semigroups of linear operators and applications to partial differential equations
• Basis property of a part of the system of eigenvectors of a holomorphic operator-function
• The essential spectrum of elliptic systems of mixed order
• Some applications of pseudo-differential operators to elasticity
• Perturbation theory for linear operators.
• Functional-differential equations in Sobolev spaces and related problems of spectral theory
• Evolutionary Integral Equations and Applications
• Operator approach to linear problems of hydrodynamics. Vol. 1: Self-adjoint problems for an ideal fluid
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