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Spectral properties of a type of integro-differential stiff problems. (English) Zbl 0566.45015
The author studies an integro-differential stiff problem in \(R^ n\), which models the vibrations of a linear viscoelastic body. The existence and uniqueness of the solution is obtained by reformulating the problem in a Hilbert space setting and showing that the corresponding operator is the infinitesimal generator of a contraction semigroup. A formal asymptotic expansion is then constructed, which converges to the solution under certain regularity conditions. Also, it is shown that the eigenvalues of two operators related to the operator of the original stiff problem are accumulation points of the spectrum of the latter.
Reviewer: C.Constanda

MSC:
45K05 Integro-partial differential equations
47D03 Groups and semigroups of linear operators
74Hxx Dynamical problems in solid mechanics
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References:
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