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On the type ofC o-semigroup associated with the abstract linear viscoelastic system

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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.

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Authors and Affiliations

  1. Center for Mathematical Sciences, Zhejiang University, 310027, Hangzhou, China

    Kangsheng Liu

  2. Dept of Mathematics and Statistics, University of Minnesota, 55812-2496, Duluth, MN, USA

    Zhuangyi Liu

Authors
  1. Kangsheng Liu
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  2. Zhuangyi Liu
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Supported partially by the Chinese Natural Science Foundation.

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Liu, K., Liu, Z. On the type ofC o-semigroup associated with the abstract linear viscoelastic system. Z. angew. Math. Phys. 47, 1–15 (1996). https://doi.org/10.1007/BF00917570

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  • DOI: https://doi.org/10.1007/BF00917570

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