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Semigroup theory and numerical approximation for equations in linear viscoelasticity. (English) Zbl 0688.65080
An integro-differential equation is considered which arises in modelling dynamic problems of viscoelastic beams. The equation is reformulated as an abstract Cauchy problem on a Hilbert space and well-posedness of the problem is proved. The construction of approximation schemes for that problem is discussed and convergence arguments are presented making use of the semigroup theory of linear operators. Numerical results are given for an example of transverse vibrations of a cantilever linear viscoelastic beam. The results of eigenvalue calculations show the efficacy of the approximation schemes.
Reviewer: Z.Dzygadło

MSC:
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
47D03 Groups and semigroups of linear operators
74Hxx Dynamical problems in solid mechanics
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