Carleman estimates for higher order partial differential operators and its applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929323959648256 |
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| author | Fu, Xiaoyu Gao, Yuan |
| author_facet | Fu, Xiaoyu Gao, Yuan |
| contents | In this paper, we obtain a Carleman estimate for the higher order partial differential operator. In the process of establishing this estimate, we developed a new method, which is called the back-propagation method (the BPM, for short). This method can also be used to build up Carleman estimates for some other partial differential operators, and might provide assistance with corresponding numerical analyses. As an application of the above-mentioned Carleman estimate, we proved the conditional stability of a Cauchy problem for a time fractional diffusion equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Carleman estimates for higher order partial differential operators and its applications Fu, Xiaoyu Gao, Yuan Analysis of PDEs Optimization and Control In this paper, we obtain a Carleman estimate for the higher order partial differential operator. In the process of establishing this estimate, we developed a new method, which is called the back-propagation method (the BPM, for short). This method can also be used to build up Carleman estimates for some other partial differential operators, and might provide assistance with corresponding numerical analyses. As an application of the above-mentioned Carleman estimate, we proved the conditional stability of a Cauchy problem for a time fractional diffusion equation. |
| title | Carleman estimates for higher order partial differential operators and its applications |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2404.14008 |