On the type of C₀-semigroup associated with the abstract linear viscoelastic system

In this paper, we give an estimate for the type of semigroup associated with an abstract equation of linear viscoelasticity when the memory kernel decays exponentially. In particular, when the kernel is of Maxwell type, we prove that the spectrum determined growth property holds. Moreover, the type of the semigroup is explicitly expressed by a formula which depends on the parameters of the kernel and the minimum spectrum point of the corresponding clastic operator.