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

#### 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

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