Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913481988505600 |
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| author | Dicke, Alexander Veselic, Ivan |
| author_facet | Dicke, Alexander Veselic, Ivan |
| contents | It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality
(a specific type of uncertainty relation).
This implies a spectral inequality for the Laplace-Beltrami operator, which, in turn, yields
observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that
are sharp in the large and in the small time regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01369 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere Dicke, Alexander Veselic, Ivan Analysis of PDEs Optimization and Control Primary 35Q93, Secondary 35K05, 93B07, 93B05 It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace-Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime. |
| title | Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere |
| topic | Analysis of PDEs Optimization and Control Primary 35Q93, Secondary 35K05, 93B07, 93B05 |
| url | https://arxiv.org/abs/2207.01369 |