On the type of \(C_ 0\)-semigroup associated with the abstract linear viscoelastic system

DOI10.1007/BF00917570zbMath0841.73026MaRDI QIDQ1909914

Zhuangyi Liu, Kangsheng Liu

Publication date: 25 July 1996

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

Hilbert spaceexponential decaymemory kernelelastic operatorkernel of Maxwell typeminimum spectrum point

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Groups and semigroups of linear operators (47D03) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Related Items (13)

On the spectrum of Euler-Bernoulli beam equation with Kelvin-Voigt damping ⋮ Lack of superstable trajectories in linear viscoelasticity: a numerical approach ⋮ Exponential stability of a flexible structure with history and thermal effect. ⋮ On uniform decay of a nonsimple thermoelastic bar with memory ⋮ Energy decay and global attractors for thermoviscoelastic systems ⋮ About analyticity for the coupled system of linear thermoviscoelastic equations ⋮ Global existence, asymptotic behavior and uniform attractors for non-autonomous thermoelastic systems ⋮ General decay of solutions of a viscoelastic equation ⋮ Global existence and asymptotic behavior of solutions for thermodiffusion equations ⋮ On the general stability of a viscoelastic wave equation with an integral condition ⋮ Global existence of the higher-dimensional linear system of thermoviscoelasticity ⋮ Property of growth determined by the spectrum of operator associated to Timoshenko system with memory ⋮ Some unexplored questions arising in linear viscoelasticity

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• On the linear stability of hyperbolic PDEs and viscoelastic flows
• An abstract Volterra equation with applications to linear viscoelasticity
• Asymptotic stability in viscoelasticity
• On the Type of Certain C^o-Semigroups
• On the Spectrum of C 0 -Semigroups
• Extensions of derivations II.
• Semigroup Theory and Numerical Approximation for Equations in Linear Viscoelasticity

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