弦网络的瞬时镇定
Finite-time stabilization of a network of strings
摘要：
研究了树形弦网络的有限时间稳定性。透明边界条件应用于所有外部节点。在任何内部节点，除了通常的连续性条件，修改基尔霍夫定律纳入阻尼项$αu_t$与系数$α$，可能取决于节点被认为是。我们表明，一个方便的选择的序列的系数$α$，任何解决方案的波动方程的网络成为常数后，有限的时间。至少对于星形树，系数的条件被证明是尖锐的。当我们用Dirichlet（resp. Neumann）边界条件。
英文摘要：
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified Kirchhoff law incorporating a damping term $αu_t$ with a coefficient $α$ that may depend on the node is considered. We show that for a convenient choice of the sequence of coefficients $α$, any solution of the wave equation on the network becomes constant after a finite time. The condition on the coefficients proves to be sharp at least for a star-shaped tree. Similar results are derived when we replace the transparent boundary condition by the Dirichlet (resp. Neumann) boundary condition at one external node.
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