论文标题
在过去的历史框架中，通过界面上的非平滑系数在过去的历史框架中与局部存储器的稳定性结果
Stability results of coupled wave models with locally memory in a past history framework via non smooth coefficients on the interface
论文作者
论文摘要
在本文中，我们研究了局部耦合波方程的稳定，其局部粘弹性阻尼仅通过非平滑系数在一个方程中起作用。首先，使用Arendt-Batty的一般标准，我们证明了系统的稳定性。其次，使用频域方法与乘数方法结合使用，我们在且仅当两个波具有相同的传播速度时，就建立了解决方案的指数稳定性。在不同的速度传播的情况下，我们证明系统的能量以1/t的速率衰减。最后，如果波传播的速度不同，我们表明缺乏指数稳定性。
In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of Arendt-Batty, we prove the strong stability of our system. Second, using a frequency domain approach combined with the multiplier method, we establish the exponential stability of the solution if and only if the two waves have the same speed of propagation. In case of different speed propagation, we prove that the energy of our system decays polynomially with rate 1/t. Finally, we show the lack of exponential stability if the speeds of wave propagation are different.
