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

2023/07/17 by Jean‐Michel Coron, Coron, Jean-Michel, Joachim Krieger +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.08329

openalex publication_date 2023/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Continuing the investigations started in the recent work [Krieger-Xiang, 2022] on semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain \mathbbS¹ and target \mathbbS^k, where \it semi-global refers to the 2π-energy bound, we prove global exact controllability of the same system for k>1 and show that the 2π-energy bound is a strict threshold for uniform asymptotic stabilization via continuous time-varying feedback laws indicating that the damping stabilization in [Krieger-Xiang, 2022] is sharp. Lastly, the global exact controllability for \mathbbS¹-target within minimum time is discussed.

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