Work

Global controllability and stabilization of the wave maps equation from a circle to a sphere

Year: 2025

Type: article

Abstract: Continuing the investigations started in the recent work (Krieger and Xiang in Semi-global controllability of a geometric wave equation, 2022. arXiv:2205.00915 ) on semi-global controllability and stabilization of the $$(1+1)$$ ( 1 + 1 ) -dimensional wave maps equation with spatial domain $$\mathbb {S}^1$$ S 1 and target $$\mathbb {S}^k$$ S k , where semi-global refers to the $$2\pi $$ 2 π -energy bound, we prove global exact controllability of the same system for $$k>1$$ k > 1 and show that the $$2\pi $$ 2 π -energy bound is a strict threshold for uniform asymptotic stabilization via continuous time-varying feedback laws indicating that the damping stabilization in Krieger and Xiang (2022) is sharp. Lastly, the global exact controllability for $$\mathbb {S}^1$$ S 1 -target within minimum time is discussed.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02961-3

Authors: Jean-Michel Coron, Joachim Krieger, Shengquan Xiang