Polynomial decay rate of C0 semigroup in Hilbert spaces. Issue 7 (3rd May 2022)

• Record Type: Journal Article
• Authors: Li, Yan-Fang; Xu, Gen-Qi
• Is Part Of: Applicable analysis. Volume 101:Issue 7(2022)
• Page Start: 2636
• Page End: 2651
• Publication Date: 2022-05-03
• Subjects: R. Triggiani; C0 semigroup -- polynomial stability -- Riesz basis -- spectrum; 47D06 -- 35B40 -- 35L20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1817399
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : 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.