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Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces. (English) Zbl 0891.35156
The authors study a second order evolution equation of the type $\stackrel{¨}{w}\left(t\right)+B\stackrel{˙}{w}\left(t\right)+Aw\left(t\right)=0$ 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.
##### MSC:
 35Q72 Other PDE from mechanics (MSC2000) 47D06 One-parameter semigroups and linear evolution equations 74B05 Classical linear elasticity
##### Keywords:
well-posedness; variational formulation