Abstract In this paper we prove stability results for a semilinear hyperbolic coupled system subject to a viscoelastic localized damping acting in the first equation and a frictional localized one acting in the second equation of the system. We divide the proof into two parts. In the first part the equations are posed in a homogeneous medium Ω with the damping acting in a boundary neighbourhood. In the second part the equations posed in an inhomogeneous medium Ω with the damping acting in a collar of the boundary and in an appropriate mesh in the interior. Due to the assumptions on the nonlinear function involving the frictional damping, general decay rates are obtained. To prove the results we used the tools of the Microlocal Analysis Theory.

中文翻译：

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具有摩擦和粘弹性局部阻尼的半线性双曲线耦合系统的稳定性

摘要 在本文中，我们证明了半线性双曲线耦合系统的稳定性结果，该系统受粘弹性局部阻尼作用在第一个方程中，摩擦局部阻尼作用在系统第二个方程中。我们将证明分为两部分。在第一部分中，方程在均匀介质 Ω 中提出，阻尼作用在边界邻域中。在第二部分中，方程在非均匀介质 Ω 中提出，阻尼作用在边界的轴环和内部的适当网格中。由于对涉及摩擦阻尼的非线性函数的假设，获得了一般衰减率。为了证明结果，我们使用了微局部分析理论的工具。