Polynomial decay rate of C0 semigroup in Hilbert spaces.

In the paper, we characterize the polynomial stability of C 0 semigroup T (t) with generator A on Hilbert space H . Let A have compact resolvent and there be a sequence of the eigenvectors of A that forms a Riesz basis for H . By the asymptotic relation of the real part and imaginary part of eigenvalues of A, we give the optimal decay rate of polynomial stability of T (t). Moreover, we give the zeros distribution of certain equations. As an application, we illustrate our general results by an acoustical system. [ABSTRACT FROM AUTHOR]