Dynamic Behavior of a One-Dimensional Wave Equation with Memory and Viscous Damping
Keyword(s):
We study the dynamic behavior of a one-dimensional wave equation with both exponential polynomial kernel memory and viscous damping under the Dirichlet boundary condition. By introducing some new variables, the time-variant system is changed into a time-invariant one. The detailed spectral analysis is presented. It is shown that all eigenvalues of the system approach a line that is parallel to the imaginary axis. The residual and continuous spectral sets are shown to be empty. The main result is the spectrum-determined growth condition that is one of the most difficult problems for infinite-dimensional systems. Consequently, an exponential stability is concluded.
2013 ◽
Vol 402
(2)
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pp. 612-625
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2019 ◽
Vol 64
(7)
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pp. 3068-3073
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2016 ◽
Vol 8
(4)
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pp. 30-30
2011 ◽
Vol 84
(2)
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pp. 381-395
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2006 ◽
Vol 229
(2)
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pp. 466-493
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2019 ◽
Vol 27
(2)
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pp. 217-223
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