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On the stability of equations with aftereffect describing dynamics of viscoelastic bodies. (Russian) Zbl 0769.73029

This paper is concerned with a linear theory of dynamic viscoelasticity for isotropic bodies. The constitutive equations have the form \(s(t)=Ce(t)+\int^ t_ 0G(t-\kappa,\tau-\kappa)e(\tau)d\tau\), where \(s\) is the stress tensor, \(t\) is the time, \(e\) is the strain tensor, \(G\) is the relaxation tensor, \(\kappa\) is a time-independent piecewise continuous and bounded function, and \(C\) is the elasticity tensor. First, energetic estimates are derived. Then the authors establish the continuous dependence of viscoelastic processes upon the body forces and surface tractions.
Reviewer: D.Ieşan (Iaşi)

MSC:

74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
35Q72 Other PDE from mechanics (MSC2000)
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