Lu, LiqingZhao, LiyanHu, Jing2022-03-102022-03-102018-11-19Lu, L., Zhao, L., & Hu, J. (2018). Effect of Kelvin-Voigt damping on spectrum analysis of a wave equation. <i>Electronic Journal of Differential Equations, 2018</i>(186), pp. 1-16.1072-6691https://hdl.handle.net/10877/15482This article concerns a one-dimensional wave equation with a small amount of Kelvin-Voigt damping. We give a detailed spectrum analysis of the system operator, from which we show that the generalized eigenfunction forms a Riesz basis for the state Hilbert space. That is, the precise and explicit expression of the eigenvalues is deduced and the spectrum-determined growth condition is established. Hence the exponential stability of the system is obtained.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalWave equationRiesz basisSpectrum-determined growth conditionKelvin-Voigt dampingArticle