Optimal control of a kinetic equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866917868574081024 |
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| author | Pim, Aaron Pryer, Tristan Trenam, Alex |
| author_facet | Pim, Aaron Pryer, Tristan Trenam, Alex |
| contents | This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal solutions exhibit a hypocoercive decay property, ensuring stability and robustness. Building on this framework, we develop a finite element discretisation that preserves the stability properties of the continuous system. The effectiveness and accuracy of the proposed method are validated through a series of numerical experiments, showcasing its ability to handle challenging PDE-constrained optimal control problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control of a kinetic equation Pim, Aaron Pryer, Tristan Trenam, Alex Numerical Analysis Optimization and Control This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal solutions exhibit a hypocoercive decay property, ensuring stability and robustness. Building on this framework, we develop a finite element discretisation that preserves the stability properties of the continuous system. The effectiveness and accuracy of the proposed method are validated through a series of numerical experiments, showcasing its ability to handle challenging PDE-constrained optimal control problems. |
| title | Optimal control of a kinetic equation |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2412.10747 |