On Dissipative Wave Equations in Hilbert-Space

Of concern is a complete linear second-order abstract Cauchy problem (ACP) on a Hilbert space. We show that under certain assumptions on the operator coefficients the associated reduction matrix generates a contraction semigroup on a scale of Hilbert spaces. This result is used to prove the well posedness of the original problem (ACP). In the Appendix we present a new proof of a perturbation result for m-accretive operators.