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Zbl 0891.35156
Liu, Kangsheng; Liu, Zhuangyi
Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces.
(English)
[J] J. Differ. Equations 141, No.2, 340-355 (1997). ISSN 0022-0396

The authors study a second order evolution equation of the type $\ddot{w}(t)+B\dot{w}(t)+Aw(t)=0$ in a Hilbert space $H$ where $A,B$ are nonnegative operators in $H$, which models a damping elastic system. A new variational formulation of the problem is introduced and well-posedness is proved by means of semigroup theory. Sufficient conditions are found for the corresponding semigroup to be analytic and differentiable.
[V.A.Liskevich (Bristol)]
MSC 2000:
*35Q72 Other PDE from mechanics
47D06 One-parameter semigroups and linear evolution equations
74B05 Classical linear elasticity

Keywords: well-posedness; variational formulation

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