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On the type ofCo-semigroup associated with the abstract linear viscoelastic system

Research paper by Kangsheng Liu, Zhuangyi Liu

Indexed on: 01 Jan '96Published on: 01 Jan '96Published in: Zeitschrift für angewandte Mathematik und Physik



Abstract

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 elastic operator.