Carleman estimates for degenerate parabolic equations with single interior point degeneracy and its applications
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910529830780928 |
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| author | Liu, Yuanhang Hu, Yaozhong Wu, Weijia Yang, Donghui |
| author_facet | Liu, Yuanhang Hu, Yaozhong Wu, Weijia Yang, Donghui |
| contents | We study the controllability of a class of $N$-dimensional degenerate parabolic equations with single interior point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then divided into two cases based on whether the degenerate point $x=0$ lies within the control region $ω_0$ or not. For each case, we establish specific Carleman estimates. As a result, we achieve null controllability in the first case $0\inω_0$ and unique continuation and approximate controllability in the second case $0\notinω_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10012 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Carleman estimates for degenerate parabolic equations with single interior point degeneracy and its applications Liu, Yuanhang Hu, Yaozhong Wu, Weijia Yang, Donghui Optimization and Control We study the controllability of a class of $N$-dimensional degenerate parabolic equations with single interior point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then divided into two cases based on whether the degenerate point $x=0$ lies within the control region $ω_0$ or not. For each case, we establish specific Carleman estimates. As a result, we achieve null controllability in the first case $0\inω_0$ and unique continuation and approximate controllability in the second case $0\notinω_0$. |
| title | Carleman estimates for degenerate parabolic equations with single interior point degeneracy and its applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2308.10012 |