Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916345920094208 |
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| author | Chorfi, S. E. Ismailov, M. I. Maniar, L. Öner, I. |
| author_facet | Chorfi, S. E. Ismailov, M. I. Maniar, L. Öner, I. |
| contents | We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the system within the framework of boundary control systems, proving its well-posedness. Then we reduce the question to a moment problem. Using the spectral analysis of the associated Sturm-Liouville problem and the moment method, we establish the null controllability of the system at any positive time $T$. Finally, we approximate minimum energy controls by a penalized HUM approach. This allows us to validate the theoretical controllability results obtained by the moment method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_01740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control Chorfi, S. E. Ismailov, M. I. Maniar, L. Öner, I. Optimization and Control Analysis of PDEs 93B05, 93C20, 42A70 We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the system within the framework of boundary control systems, proving its well-posedness. Then we reduce the question to a moment problem. Using the spectral analysis of the associated Sturm-Liouville problem and the moment method, we establish the null controllability of the system at any positive time $T$. Finally, we approximate minimum energy controls by a penalized HUM approach. This allows us to validate the theoretical controllability results obtained by the moment method. |
| title | Boundary null controllability of the heat equation with Wentzell boundary condition and Dirichlet control |
| topic | Optimization and Control Analysis of PDEs 93B05, 93C20, 42A70 |
| url | https://arxiv.org/abs/2408.01740 |