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

Zhuangyi Liu; Qiong Zhang

doi:10.1007/s00033-015-0517-y

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

Zhuangyi Liu, Qiong Zhang

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

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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 c^Aαu≤Bu≤C^Aαu 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 language	English (US)
Pages (from-to)	1799-1804
Number of pages	6
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s00033-015-0517-y
State	Published - Aug 10 2015

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Publisher Copyright:
© 2015, Springer Basel.

Keywords

35B40
47D03
93D05

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

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