Polynomial Stability of Semigroups Generated by Operator Matrices

In this paper we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable semigroups. As our main results, we present conditions under which also the semigroup generated by the operator matrix is polynomially stable. The theoretic results are applied to deriving conditions for the polynomial stability of a system consisting of a two-dimensional and a one-dimensional damped wave equations.