Stability of the wave equations on a tree with local Kelvin–Voigt damping

Kaïs Ammari, Zhuangyi Liu, Farhat Shel

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at the vertices of the tree, exponential/polynomial stability are proved. Our results generalize the case of single elastic string with local Kelvin–Voigt damping in Liu and Rao (Z. Angew Math Phys 56:630–644, 2005), Liu and Liu (Z. Angew Math Phys 53:265–280, 2002).

Original languageEnglish (US)
Pages (from-to)364-382
Number of pages19
JournalSemigroup Forum
Volume100
Issue number2
DOIs
StatePublished - Apr 1 2020

Keywords

  • Dissipative wave operator
  • Frequency approach
  • Kelvin–Voigt damping
  • Tree

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