In this paper, we consider the Cauchy–Ventcel problem in an inhomogeneous medium with dynamic boundary conditions subject to a nonlinear damping distributed around a neighborhood [Formula: see text] of the boundary according to the Geometric Control Condition. Uniform decay rates of the associated energy are established and, in addition, the exact internal controllability for the linear problem is also proved. For this purpose, refined microlocal analysis arguments are considered by exploiting ideas due to Burq and Gérard [Contrôle Optimal des équations aux dérivées partielles. (2001); http://www.math.upsud.fr/burq/articles/coursX.pdf ].

中文翻译：

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具有局部分布非线性阻尼和动态柯西-文塞尔型边界条件的非均匀介质中半线性波动方程的均匀稳定

在本文中，我们根据几何控制条件考虑在具有动态边界条件的非均匀介质中的 Cauchy-Ventcel 问题，该问题受到非线性阻尼的影响，该非线性阻尼分布在边界的邻域 [公式：见文本] 周围。建立了相关能量的均匀衰减率，此外，还证明了线性问题的精确内部可控性。为此，通过利用 Burq 和 Gérard [Contrôle Optimal des équations aux derivées partielles. (2001); http://www.math.upsud.fr/burq/articles/coursX.pdf ]。