In this paper we consider an anisotropic and inhomogeneous viscoelastic body that is subjected on the time interval [0,T] to body forces and initial and boundary data having a bounded support. Then a complete description is given upon what happen in the outside of the support region D_T of the data. More precisely, when the genuine dynamic linear viscoelasticity is considered, we prove that, for each t ∈[0,T], there exists a bounded domain D_ct, so that the whole activity vanishes in the outside of D_ct; while into the region D_ct/D_T an appropriate measure of the dynamic viscoelastic process in question decays spatially with the distance r from the bounded support D_T, the decay rate being controlled by the factor (1 - r/ct).
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