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arXiv · 2205.00915

Semi-global controllability of a geometric wave equation

Joachim Krieger·Shengquan Xiang
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Abstract

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 $2\pi$, 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 $k=1$.

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Joachim Krieger, Shengquan Xiang. 2022-05-02. Semi-global controllability of a geometric wave equation. https://arxiv.org/abs/2205.00915

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