We consider a wave equation with a structural damping coupled with an undamped wave equation located at its boundary. We prove that, due to the coupling, the full system is parabolic. In order to show that the underlying operator generates an analytical semigroup, we study in particular the effect of the damping of the “interior” wave equation on the “boundary” wave equation and show that it generates a structural damping.

中文翻译：

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对应于具有 Ventcel 边界条件的强阻尼波动方程的半群的解析性

我们考虑具有结构阻尼的波动方程及其边界处的无阻尼波动方程。我们证明，由于耦合，整个系统是抛物线的。为了表明基础算子产生了一个解析半群，我们特别研究了“内部”波动方程的阻尼对“边界”波动方程的影响，并表明它产生了结构阻尼。