Frequency domain approach for the polynomial stability of a system of partially damped wave equations

Zhuangyi Liu, Bopeng Rao

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.

Original languageEnglish (US)
Pages (from-to)860-881
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume335
Issue number2
DOIs
StatePublished - Nov 15 2007

Keywords

  • Frequency domain
  • Indirect damping
  • Polynomial decay rate

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