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Asymptotic stability of wave equations coupled by velocities

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  • This paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient and necessary condition, that the coefficients satisfy, leading to the exponential stability of the system. In addition, we give the optimal decay rate in one dimensional case.
    Mathematics Subject Classification: Primary: 93B05, 93D15; Secondary: 35L04.


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