Controllability and Inverse Problems for Parabolic Systems with Dynamic Boundary Conditions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917776911761408 |
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| author | Chorfi, S. E. Maniar, L. |
| author_facet | Chorfi, S. E. Maniar, L. |
| contents | This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to prove null controllability for parabolic systems and Lipschitz stability estimates for inverse problems with dynamic boundary conditions of surface diffusion type. We mainly focus on the substantial difficulties compared to static boundary conditions. Finally, some conclusions and open problems will be mentioned. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Controllability and Inverse Problems for Parabolic Systems with Dynamic Boundary Conditions Chorfi, S. E. Maniar, L. Optimization and Control Analysis of PDEs 93B05, 93B07, 35R30, 35R25, 35K20 This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to prove null controllability for parabolic systems and Lipschitz stability estimates for inverse problems with dynamic boundary conditions of surface diffusion type. We mainly focus on the substantial difficulties compared to static boundary conditions. Finally, some conclusions and open problems will be mentioned. |
| title | Controllability and Inverse Problems for Parabolic Systems with Dynamic Boundary Conditions |
| topic | Optimization and Control Analysis of PDEs 93B05, 93B07, 35R30, 35R25, 35K20 |
| url | https://arxiv.org/abs/2409.10302 |