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Qualitative properties of certain \(C_0\) semigroups arising in elastic systems with various dampings. (English) Zbl 0962.47020

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.

MSC:

47D06 One-parameter semigroups and linear evolution equations
35B40 Asymptotic behavior of solutions to PDEs
34G10 Linear differential equations in abstract spaces
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