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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.11624 |
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| _version_ | 1866911673194905600 |
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| author | de Hoop, Maarten V. Kykkänen, Antti Trélat, Emmanuel |
| author_facet | de Hoop, Maarten V. Kykkänen, Antti Trélat, Emmanuel |
| contents | We develop a deterministic large-time mechanism yielding Ces{à}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact measured homogeneous space replaces full observation on the whole observation manifold by a finite convex combination of translates of one prototype subset. A switching realization theorem then turns that static design into a genuinely moving observer, while a Hilbertian tail-reduction proposition shows that interval estimates proved only on growing spectral windows still recover the full conserved energy after Ces{à}ro averaging. The resulting design-to-observability chain applies to interior observations for wave, Klein-Gordon, and Schr{ö}dinger equations on compact measured homogeneous manifolds, to moving boundary caps on the Euclidean ball, and to a singular almost-separated gas-giant boundary model. The framework is especially relevant when each instantaneous observation set is too small for one to expect a finite-time GCC or time-dependent GCC statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11624 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moving localized observations and Ces{à}ro asymptotic observability for conservative PDEs de Hoop, Maarten V. Kykkänen, Antti Trélat, Emmanuel Analysis of PDEs We develop a deterministic large-time mechanism yielding Ces{à}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact measured homogeneous space replaces full observation on the whole observation manifold by a finite convex combination of translates of one prototype subset. A switching realization theorem then turns that static design into a genuinely moving observer, while a Hilbertian tail-reduction proposition shows that interval estimates proved only on growing spectral windows still recover the full conserved energy after Ces{à}ro averaging. The resulting design-to-observability chain applies to interior observations for wave, Klein-Gordon, and Schr{ö}dinger equations on compact measured homogeneous manifolds, to moving boundary caps on the Euclidean ball, and to a singular almost-separated gas-giant boundary model. The framework is especially relevant when each instantaneous observation set is too small for one to expect a finite-time GCC or time-dependent GCC statement. |
| title | Moving localized observations and Ces{à}ro asymptotic observability for conservative PDEs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.11624 |