Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains

Jingrui Niu; Shengquan Xiang

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arXiv · 2610.35610

Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains

Jingrui Niu·Shengquan Xiang

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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.

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BibTeX RIS

Jingrui Niu, Shengquan Xiang. 2026-10-26. Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains. https://arxiv.org/abs/2610.35610

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