G. Chen and D. L. Russell [(*) A mathematical model for linear elastic systems with structural damping, MRC Technical summary Report 2089, Math. Res. Center. Univ. Wisconsin-Madison (1980)] studied the following linear elastic systems with structural damping
where means , , a Hilbert space with inner product ( and associated with , A and B are positive definite self-adjoint unbounded linear operators on H and B is -bounded. Letting , , we get the equivalent first order linear systems
G. Chen and D. L. Russel (*) have proved that generates a holomorphic semigroup, if some addition conditions are satisfied. Moreover, they still conjectured that if A and B are positive definite self-adjoint unbounded linear operators with the domain , such that
then should generate a holomorphic semi-group, where and are positive constant numbers with . Also some partial results for conjecture (I) and (II) are shown in (*). Recently, the author gave an answer to the conjecture (I) affirmatively [A problem for linear elastic systems with structural damping (to appear)]. In this paper we will show that conjecture (II) is also true.