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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 w ¨(t)+Bw ˙(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.
MSC:
35Q72Other PDE from mechanics (MSC2000)
47D06One-parameter semigroups and linear evolution equations
74B05Classical linear elasticity