Carleman Inequalities for the Heat Equation with Fourier Boundary Conditions: Applications to Null Controllability Problems
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908837419679744 |
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| author | Villa, Jose Antonio |
| author_facet | Villa, Jose Antonio |
| contents | In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_νy+by=f1_γ$, where the control acts on a small portion $γ$ of the boundary. We apply this inequality to address the null controllability problem with boundary control supported on this small region. An explicit solution to this problem is obtained via a system of coupled parabolic equations. Based on these results, we propose an iterative numerical method to solve the coupled system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Carleman Inequalities for the Heat Equation with Fourier Boundary Conditions: Applications to Null Controllability Problems Villa, Jose Antonio Optimization and Control Analysis of PDEs 35K, 35Q, 49K20, 49N15 In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_νy+by=f1_γ$, where the control acts on a small portion $γ$ of the boundary. We apply this inequality to address the null controllability problem with boundary control supported on this small region. An explicit solution to this problem is obtained via a system of coupled parabolic equations. Based on these results, we propose an iterative numerical method to solve the coupled system. |
| title | Carleman Inequalities for the Heat Equation with Fourier Boundary Conditions: Applications to Null Controllability Problems |
| topic | Optimization and Control Analysis of PDEs 35K, 35Q, 49K20, 49N15 |
| url | https://arxiv.org/abs/2602.15300 |