论文标题
几何波方程的半全球可控性
Semi-global controllability of a geometric wave equation
论文作者
论文摘要
我们证明了$（1+1）$ - 尺寸波映射方程，带有空间域$ \ mathbb {s}^1 $和目标$ \ mathbb {s}^k $。首先，我们表明，当能量严格低于阈值$2π$时，阻尼可以稳定系统，在该阈值$2π$中，谐波图似乎是全球稳定的阻塞。然后，我们调整迭代控制程序，以获得波浪图方程的低能确切可控性。在情况下，此结果是最佳的。$ k = 1 $。
We prove the semi-global controllability and stabilization of the $(1+1)$-dimensional wave maps equation with spatial domain $\mathbb{S}^1$ and target $\mathbb{S}^k$. First we show that damping stabilizes the system when the energy is strictly below the threshold $2π$, where harmonic maps appear as obstruction for global stabilization. Then, we adapt an iterative control procedure to get low-energy exact controllability of the wave maps equation. This result is optimal in the case $k=1$.
