In this paper, we study the stability problem of a star-shaped network of elastic strings with a local Kelvin-Voigt damping. Under the assumption that the damping coefficients have some singularities near the transmission point, we prove that the semigroup corresponding to the system is polynomially stable and the decay rates depend on the speed of the degeneracy. This result improves the decay rate of the semigroup associated to the system on an earlier result of Z. Liu and Q. Zhang in [21] involving the wave equation with local Kelvin-Voigt damping and non-smooth coefficient at interface.

中文翻译：

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具有局部 Kelvin-Voigt 阻尼和界面非光滑系数的星形网络的稳定性

在本文中，我们研究了具有局部 Kelvin-Voigt 阻尼的星形弹性弦网络的稳定性问题。在阻尼系数在传输点附近具有奇点的假设下，我们证明了系统对应的半群是多项式稳定的，衰减率取决于退化的速度。该结果改进了与系统相关的半群的衰减率，这是基于 Z. Liu 和 Q. Zhang 在 [21] 中的早期结果，涉及具有局部 Kelvin-Voigt 阻尼和界面非光滑系数的波动方程。