Observability properties of the singular Grushin equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910015641616384 |
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| author | Vanlaere, Roman |
| author_facet | Vanlaere, Roman |
| contents | We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some specific configurations of the observation set, we obtain the exact minimal time of observability. The analysis we present relies on recent Carleman estimates obtained by K. Beauchard, J. Dardé, and S. Ervedoza. As a byproduct of these results, we observe, for the heat equation associated to the Laplace-Beltrami operator on almost-Riemannian manifolds, a dependence of the minimal time of observability on the dimension of the singularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_08044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Observability properties of the singular Grushin equation Vanlaere, Roman Analysis of PDEs Optimization and Control 93B05, 93B07, 93C20, 35K65, 35K67 We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some specific configurations of the observation set, we obtain the exact minimal time of observability. The analysis we present relies on recent Carleman estimates obtained by K. Beauchard, J. Dardé, and S. Ervedoza. As a byproduct of these results, we observe, for the heat equation associated to the Laplace-Beltrami operator on almost-Riemannian manifolds, a dependence of the minimal time of observability on the dimension of the singularity. |
| title | Observability properties of the singular Grushin equation |
| topic | Analysis of PDEs Optimization and Control 93B05, 93B07, 93C20, 35K65, 35K67 |
| url | https://arxiv.org/abs/2602.08044 |