In this paper, we consider a coupled system of two wave equations. One of these equations is conservative, and the other has damping and delay terms. If the damping acts with more force than the delay term, we show polynomial stability for strong solutions of the system. Explicit decay rates are found, and the optimality of those rates is discussed. On the other hand, if the damping acts with the same or less force than the delay term, then we obtain a result of instability by constructing a sequence of time delays and initial data such that the solutions are not asymptotically stable.

中文翻译：

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带延迟项的耦合波的稳定性和不稳定性结果

在本文中，我们考虑两个波动方程的耦合系统。这些方程之一是保守的，另一个具有阻尼和延迟项。如果阻尼的作用力大于延迟项，我们将显示系统强解的多项式稳定性。发现了显式衰减率，并讨论了这些率的最优性。另一方面，如果阻尼作用与延迟项相同或更少的力，那么我们通过构造时间延迟和初始数据的序列来获得不稳定的结果，使得解不是渐近稳定的。