Krieger, JoachimXiang, Shengquan2022-05-032022-05-032022-05-032022-05-0210.48550/arXiv.2205.00915https://infoscience.epfl.ch/handle/20.500.14299/1875452205.00915v1We prove the semi-global controllability and stabilization of the $(1+1)-$dimensional wave maps equation with spatial domain 𝕊1 and target $𝕊k$. 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 $k=1$.wave mapssemi-global controllabilitystabilizationquantitativetext::journal::journal article::research article