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

^*此作品的通讯作者

数学学院

University of Minnesota Duluth

科研成果: 期刊稿件 › 文章 › 同行评审

22 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1799-1804
页数	6
期刊	Zeitschrift fur Angewandte Mathematik und Physik
卷	66
期	4
DOI	https://doi.org/10.1007/s00033-015-0517-y
出版状态	已出版 - 10 8月 2015

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

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