Local controllability and non-controllability for a 1D wave equation with bilinear control
Local controllability and non-controllability for a 1D wave equation with bilinear control
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DOI：
10.1016/j.jde.2010.10.008
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发表时间：
2011-02
影响因子：
2.4
通讯作者：
K. Beauchard
中科院分区：
文献类型：
--
作者：
K. Beauchard
考虑在区间（0,1）上具有双线性控制和Neumann边界条件的线性波动方程。我们研究了这种非线性控制系统的可控性，局部围绕一个恒定的参考轨迹。我们证明下列结果一般成立。这些结果的证明依赖于逆映射定理和二阶展开式。
We consider a linear wave equation, on the interval (0,1), with bilinear control and Neumann boundary conditions. We study the controllability of this nonlinear control system, locally around a constant reference trajectory. We prove that the following results hold generically. The proof of these results relies on the inverse mapping theorem and second order expansions.