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.

中文翻译：

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速度耦合波动方程的渐近稳定性

本文致力于研究具有速度耦合的常系数波动方程的渐近稳定性。通过分别采用Riesz基法、乘法器法和频域法，我们找到了系数满足的充分必要条件，从而导致系统的指数稳定性。此外，我们给出了一维情况下的最佳衰减率。