Abstract
In the paper, we characterize the polynomial stability of semigroup with generator A on Hilbert space . Let A have compact resolvent and there be a sequence of the eigenvectors of A that forms a Riesz basis for . 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 . Moreover, we give the zeros distribution of certain equations. As an application, we illustrate our general results by an acoustical system.
COMMUNICATED BY:
Disclosure statement
No potential conflict of interest was reported by the author(s).