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Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains
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 R2 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.
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BibTeX
@misc{niu2026asymptotic,
title = {{Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains}},
author = {Jingrui Niu and Shengquan Xiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35610},
eprint = {2610.35610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35610},
}
RIS
TY - UNPB
TI - Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains
AU - Jingrui Niu
AU - Shengquan Xiang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35610
UR - https://arxiv.org/abs/2610.35610
AB - 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.
ER -