SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 1973-1988, January 2021.
The stabilization of a multidimensional wave equation on a cuboidal domain is considered. By applying the localized Kelvin--Voigt damping, in a region where the geometric control condition (GCC) is not satisfied, we prove that the system can be polynomially stabilized to 0 with the polynomial decay rate $t^{-\frac{1}{3}}$ under smooth initial conditions. In particular, the optimality of this explicit decay rate is verified for this system through a careful resolvent estimate.

中文翻译：

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立方域波动方程的开尔文镇定--Voigt阻尼：一个没有几何控制条件的情况

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 1973-1988 页，2021
年1 月。考虑了立方体域上多维波动方程的稳定性。通过应用局部开尔文-Voigt 阻尼，在不满足几何控制条件（GCC）的区域，我们证明系统可以多项式稳定到 0，多项式衰减率 $t^{-\frac{1 }{3}}$ 在平滑的初始条件下。特别是，通过仔细的解析度估计验证了该系统的显式衰减率的最优性。