Analyticity and Differentiability of Semigroups Associated with Elastic Systems with Damping and Gyroscopic Forces

In this paper, we consider a second order variational evolution equation in a Hilbert space, which can model an elastic system with damping and gyroscopic forces. A new form of the corresponding first order evolution equation is introduced, and its well-posedness is proved by means of the semigroup theory. We give sufficient conditions for analyticity and differentiablity of the associated semigroup. The results are applied to several PDEs with discontinuous coefficients and mechanical boundary conditions. It is proved that Russell's spacial hysteresis model of a vibrating beam [22] is associated with an exponentially stable, analytic semigroup.