Effect of Kelvin-Voigt damping on spectrum analysis of a wave equation

Abstract

This 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.