Semi-global controllability of a geometric wave equation

Abstract

We prove the semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain S 1 and target 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.