Advances in Differential Equations

Qualitative properties of certain $C_0$ semigroups arising in elastic systems with various dampings

Zhuangyi Liu and Jiongmin Yong

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Abstract

This paper studies various qualitative properties, such as exponential stability, spectrum determining growth property, differentiability, of Gevrey class and analyticity, for the semigroup $e^{\mathcal{At}}$ generated by the operator of the form $\mathcal{A}=\begin{pmatrix} -A_0 & {B}\cr {C}& {-A_1} \end{pmatrix}$, where both $-A_0$ and $-A_1$ generate contraction semigroups on some Hilbert spaces, and $B$ and $C$ are certain closed densely defined linear operators.

Article information

Source
Adv. Differential Equations Volume 3, Number 5 (1998), 643-686.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366292557

Mathematical Reviews number (MathSciNet)
MR1665862

Zentralblatt MATH identifier
0962.47020

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35B99: None of the above, but in this section 73D30

Citation

Liu, Zhuangyi; Yong, Jiongmin. Qualitative properties of certain $C_0$ semigroups arising in elastic systems with various dampings. Adv. Differential Equations 3 (1998), no. 5, 643--686. https://projecteuclid.org/euclid.ade/1366292557.


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