Observability from measurable sets for strongly coupled parabolic systems via single-component observation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913033699196928 |
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| author | Fu, Xiaoyu Wang, Gengsheng Yu, Huaiqiang Zhu, Xiaomin |
| author_facet | Fu, Xiaoyu Wang, Gengsheng Yu, Huaiqiang Zhu, Xiaomin |
| contents | We establish an observability inequality from space-time measurable sets for a class of strongly coupled parabolic systems consisting of two equations, where the observation acts on a single-component. The model is motivated by parabolic equations with complex coefficients and serves as a prototypical example of strongly coupled systems. The main difficulty lies in the fact that, unlike in the scalar and weakly coupled cases, pointwise-in-time interpolation observability estimates fail, as the observed component may exhibit high-frequency oscillatory cancellations induced by the coupling. To overcome this difficulty, we develop a new integral-type interpolation observability inequality based on a Remez-type inequality. With the aid of this integral-type interpolation observability inequality and the strategy developed in [Phung and Wang, JEMS, (2013), 681--703] and [Apraiz, Escauriaza,Wang and Zhang, JEMS, (2014), 2433--2475] for deriving observability from measurable sets, we obtain the desired observability inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13599 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Observability from measurable sets for strongly coupled parabolic systems via single-component observation Fu, Xiaoyu Wang, Gengsheng Yu, Huaiqiang Zhu, Xiaomin Optimization and Control Mathematical Physics 35K40, 93B07, 93C20, 49J20 We establish an observability inequality from space-time measurable sets for a class of strongly coupled parabolic systems consisting of two equations, where the observation acts on a single-component. The model is motivated by parabolic equations with complex coefficients and serves as a prototypical example of strongly coupled systems. The main difficulty lies in the fact that, unlike in the scalar and weakly coupled cases, pointwise-in-time interpolation observability estimates fail, as the observed component may exhibit high-frequency oscillatory cancellations induced by the coupling. To overcome this difficulty, we develop a new integral-type interpolation observability inequality based on a Remez-type inequality. With the aid of this integral-type interpolation observability inequality and the strategy developed in [Phung and Wang, JEMS, (2013), 681--703] and [Apraiz, Escauriaza,Wang and Zhang, JEMS, (2014), 2433--2475] for deriving observability from measurable sets, we obtain the desired observability inequality. |
| title | Observability from measurable sets for strongly coupled parabolic systems via single-component observation |
| topic | Optimization and Control Mathematical Physics 35K40, 93B07, 93C20, 49J20 |
| url | https://arxiv.org/abs/2604.13599 |