论文标题
具有双曲线边界条件的波动方程：频域方法
Wave equation with hyperbolic boundary condition: a frequency domain approach
论文作者
论文摘要
在本文中，我们研究了线性波方程的稳定性，其中边界的一个部分（被视为较低维度的riemannian歧管）受耦合波方程的控制，而另一部分则受到散发性的robin速度反馈。我们证明，闭环方程在合适的能量空间上产生了线性收缩的半均匀稳定的半群。此外，在乘数相关的几何条件下，我们为强溶液建立了多项式衰减率。这是通过估计分解算子在假想轴上的生长来实现的。
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a dissipative Robin velocity feedback. We prove that the closed-loop equations generate a semi-uniformly stable semigroup of linear contractions on a suitable energy space. Furthermore, under multiplier-related geometrical conditions, we establish a polynomial decay rate for strong solutions. This is achieved by estimating the growth of the resolvent operator on the imaginary axis.
