Liu, Zhuangyi; Yong, Jiongmin Qualitative properties of certain \(C_0\) semigroups arising in elastic systems with various dampings. (English) Zbl 0962.47020 Adv. Differ. Equ. 3, No. 5, 643-686 (1998). This paper studies various qualitative properties, such as exponential stability, spectrum determining growth property, differentiability, of Gevrey class and analyticity, for the semigroup \(e^{{\mathcal A}t}\) generated by the operator of the form \[ {\mathcal A}= \begin{pmatrix} -A_0 & B\\ C & -A_1\end{pmatrix}, \] 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. Reviewer: A.V.Balakrishnan (Los Angeles) Cited in 20 Documents MSC: 47D06 One-parameter semigroups and linear evolution equations 35B40 Asymptotic behavior of solutions to PDEs 34G10 Linear differential equations in abstract spaces Keywords:exponential stability; spectrum determining growth property; differentiability; Gevrey class; analyticity PDFBibTeX XMLCite \textit{Z. Liu} and \textit{J. Yong}, Adv. Differ. Equ. 3, No. 5, 643--686 (1998; Zbl 0962.47020)