Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914659406184448 |
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| author | Khodja, F. Ammar Benabdallah, A. González-Burgos, M. Morancey, M. |
| author_facet | Khodja, F. Ammar Benabdallah, A. González-Burgos, M. Morancey, M. |
| contents | This paper investigates the link between the null controllability property for some abstract parabolic problems and an inequality that can be seen as a quantified Fattorini-Hautus test. Depending on the hypotheses made on the abstract setting considered we prove that this inequality either gives the exact minimal null control time or at least gives the qualitative property of existence of such a minimal time. We also prove that for many known examples of minimal time in the parabolic setting, this inequality recovers the value of this minimal time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems Khodja, F. Ammar Benabdallah, A. González-Burgos, M. Morancey, M. Optimization and Control 93C20, 93B05, 93C25 This paper investigates the link between the null controllability property for some abstract parabolic problems and an inequality that can be seen as a quantified Fattorini-Hautus test. Depending on the hypotheses made on the abstract setting considered we prove that this inequality either gives the exact minimal null control time or at least gives the qualitative property of existence of such a minimal time. We also prove that for many known examples of minimal time in the parabolic setting, this inequality recovers the value of this minimal time. |
| title | Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems |
| topic | Optimization and Control 93C20, 93B05, 93C25 |
| url | https://arxiv.org/abs/2401.17051 |