Abstract
In this paper, we study the stability of a system of wave equations which are weakly coupled and partially damped. Using a frequency domain approach based on the growth of the resolvent on the imaginary axis, we establish the polynomial energy decay rate for smooth initial data. We show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations.
Original language | English (US) |
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Pages (from-to) | 860-881 |
Number of pages | 22 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 335 |
Issue number | 2 |
DOIs | |
State | Published - Nov 15 2007 |
Keywords
- Frequency domain
- Indirect damping
- Polynomial decay rate