A note on the polynomial stability of a weakly damped elastic abstract system

Zhuangyi Liu, Qiong Zhang

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, we analyze the following abstract system (Formula Presented.) where A is a self-adjoint, positive definite operator on a Hilbert space H, B (the dissipation operator) is another positive operator satisfying cu≤Bu≤Cu for some constants 0 <  c <  C. The case of 0≤α≤1 has been well investigated in the literature. Our contribution is to prove that the associated semigroup is polynomially stable when α<0. Moreover, we obtain the optimal order of polynomial stability.

Original languageEnglish (US)
Pages (from-to)1799-1804
Number of pages6
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume66
Issue number4
DOIs
StatePublished - Aug 10 2015
Externally publishedYes

Fingerprint

Damped
Mathematical operators
polynomials
Polynomials
operators
Polynomial
Hilbert spaces
Positive Operator
Operator
Positive definite
Dissipation
Semigroup
Hilbert space
dissipation

Keywords

  • 35B40
  • 47D03
  • 93D05

Cite this

A note on the polynomial stability of a weakly damped elastic abstract system. / Liu, Zhuangyi; Zhang, Qiong.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 66, No. 4, 10.08.2015, p. 1799-1804.

Research output: Contribution to journalArticle

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