Effect of Kelvin-Voigt damping on spectrum analysis of a wave equation
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Date
2018-11-19
Authors
Lu, Liqing
Zhao, Liyan
Hu, Jing
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Wave equation, Riesz basis, Spectrum-determined growth condition, Kelvin-Voigt damping
Citation
Lu, 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.
Rights
Attribution 4.0 International