Stability of a string with local Kelvin-Voigt damping and nonsmooth coefficient at interface

Zhuangyi Liu, Qiong Zhang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper, we study the stability of an elastic string system with local Kelvin Voigt damping. Few results for this system are known in the literature. Under the assumption that the damping coefficient has a singularity at the interface of the damped and undamped regions and behaves like xα near the interface, we prove that the semigroup corresponding to the system is polynomially or exponentially stable and the decay rate depends on the parameter α ∈ (0, 1].

Original languageEnglish (US)
Pages (from-to)1859-1871
Number of pages13
JournalSIAM Journal on Control and Optimization
Volume54
Issue number4
DOIs
StatePublished - Jan 1 2016

Keywords

  • C semigroup
  • Exponential stability
  • Kelvin-Voigt damping
  • Polynomial stability

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