Exact Controllability of the 1-D Wave Equation on Finite Metric Tree Graphs
Exact Controllability of the 1-D Wave Equation on Finite Metric Tree Graphs
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DOI：
10.1007/s00245-019-09629-3
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发表时间：
2019-11
影响因子：
1.8
通讯作者：
S. Avdonin;Yuanyuan Zhao
中科院分区：
文献类型：
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作者：
S. Avdonin;Yuanyuan Zhao
本文考虑有限度量图上波动方程的初边值问题和具有Dirichlet边界控制的控制问题。我们提出了新的构造性算法求解一般图的初边值问题和树图的边界控制问题。我们证明了树上的波动方程是完全可控的，当且仅当控制施加在所有或所有，但一个边界顶点。我们找到了最小能控时间，并证明了我们的结果在一般情况下是最优的。形状和速度可控性的证明是纯动力学的，而完全可控性的证明同时使用动力学和矩量法方法。
In this paper, we consider initial boundary value problems and control problems for the wave equation on finite metric graphs with Dirichlet boundary controls. We propose new constructive algorithms for solving initial boundary value problems on general graphs and boundary control problems on tree graphs. We demonstrate that the wave equation on a tree is exactly controllable if and only if controls are applied at all or all but one of the boundary vertices. We find the minimal controllability time and prove that our result is optimal in the general case. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the full controllability utilizes both dynamical and moment method approaches.