Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains
Year: 2026
Type: preprint
Abstract: Continuing \cite{NWX} and Part I \cite{AOSI}, we further investigate symmetry for spacetime observability of wave equations. Building on asymptotic observable symmetry (AOS) introduced in \cite{AOSI}, we study symmetry under glancing propagation and caustics. We prove that, on every smooth bounded domain in $\R^2$ and for every positive observation time, there is a fixed measurable set satisfying the essential spacetime measurable geometric control condition. However, the observability inequality fails on this set.
Source: arXiv (Cornell University)
Authors: Niu, Jingrui, Xiang, Shengquan
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223892734