Carleman estimate for full-discrete approximations of the complex Ginzburg-Landau equation with dynamic boundary conditions and applications to controllability
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916663062953984 |
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| author | Zhu, Xu Zhou, Wenwen Wu, Bin |
| author_facet | Zhu, Xu Zhou, Wenwen Wu, Bin |
| contents | In this paper, we investigate Carleman estimate and controllability result for the fully-discrete approximations of a one-dimensional Ginzburg-Landau equation with dynamic boundary conditions. We first establish a new discrete Carleman estimate for the corresponding adjoint system. Based on this Carleman estimate, we obtain a relaxed observability inequality for the adjoint system, and then a controllability result for the fully-discrete Ginzburg-Landau equation with dynamic boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleman estimate for full-discrete approximations of the complex Ginzburg-Landau equation with dynamic boundary conditions and applications to controllability Zhu, Xu Zhou, Wenwen Wu, Bin Analysis of PDEs In this paper, we investigate Carleman estimate and controllability result for the fully-discrete approximations of a one-dimensional Ginzburg-Landau equation with dynamic boundary conditions. We first establish a new discrete Carleman estimate for the corresponding adjoint system. Based on this Carleman estimate, we obtain a relaxed observability inequality for the adjoint system, and then a controllability result for the fully-discrete Ginzburg-Landau equation with dynamic boundary conditions. |
| title | Carleman estimate for full-discrete approximations of the complex Ginzburg-Landau equation with dynamic boundary conditions and applications to controllability |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.20628 |