Exponential decay of solution energy for equations associated with some operator models of mechanics

We consider the equation (x) double over dot + B(x) over dot + Ax = 0 in a Hilbert space H, where A is a uniformly positive self-adjoint operator and B is a dissipative operator. The main result is the proof of a theorem stating the exponential energy decay for solutions of this equation (or the exponential stability of the semigroup associated with the equation) under the additional assumption that B is sectorial and is subordinate to A in the sense of quadratic forms.