On the Mathematical Model for Linear Elastic Systems with Analytic Damping

Source abstract

In the present paper we investigate linear elastic systems with damping $\ddot y + B\dot y + Ay = 0$ in Hilbert spaces, where A is a positive definite unbounded linear operator and B is a closed linear operator related in various ways to $A^\alpha (\frac{1}{2} \leqq \alpha \leqq 1)$. We discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems.