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Zbl 0659.34054
Huang, Falun; Liu, Kangsheng
Holomorphic property and exponential stability of the semigroup associated with linear elastic systems with damping. (English)
[J] Ann. Differ. Equations 4, No.4, 410-424 (1988). ISSN 1002-0942

We investigate the analytic property and the exponential stability for linear elastic systems with damping ÿ$+B\dot y+Ay=0$ in Hilbert spaces, where A is a positive definite unbounded linear operator and B is a closed linear operator related in various ways to $A\sp{\alpha}$ ($\le \alpha \le 1)$. We obtain some fundamental results for the holomorphic property and the exponential stability of the semigroup associated with these systems.

MSC 2000:: *34D05 Asymptotic stability of ODE
34G10 Linear ODE in abstract spaces
34A30 Linear ODE and systems

Keywords: exponential stability; linear elastic systems with damping; Hilbert spaces

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