Liqing Lu, Liyan Zhao, Jing Hu
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.
Submitted September 9, 2018. Published November 19, 2018.
Math Subject Classifications: 35L05, 93C20, 35B35.
Key Words: Wave equation; Riesz basis; spectrum-determined growth condition;
Kelvin-Voigt damping.
Show me the PDF file (236 KB), TEX file for this article.
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Liqing Lu School of mathematical sciences Shanxi University Taiyuan 030006, China email: lulq@sxu.edu.cn |
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Liyan Zhao School of mathematical sciences Shanxi University Taiyuan 030006, China email: 494531816@qq.com |
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Jing Hu School of mathematical sciences Shanxi University Taiyuan 030006, China email: 1556357154@qq.com |
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