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.
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