Characterization of polynomial decay rate for the solution of linear evolution equation

Zhuangyi Liu, Bopeng Rao

Research output: Contribution to journalArticlepeer-review

150 Scopus citations

Abstract

In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be unbounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not exponentially stable systems to obtain the decay rate, which is not available in the literature.

Original languageEnglish (US)
Pages (from-to)630-644
Number of pages15
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume56
Issue number4
DOIs
StatePublished - Jul 2005

Keywords

  • Frequency domain
  • Polynomial decay rate
  • Semigroup

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