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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.23154 |
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| _version_ | 1866915782396477440 |
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| author | Boutaayamou, Idriss Et-tahri, Fouad Maniar, Lahcen Periago, Francisco |
| author_facet | Boutaayamou, Idriss Et-tahri, Fouad Maniar, Lahcen Periago, Francisco |
| contents | This paper addresses the exact controllability of trajectories in the one-dimensional Fisher-Stefan problem--a reaction-diffusion equation that models the spatial propagation of biological, chemical, or physical populations within a free-end domain, governed by Stefan's law. We establish the local exact controllability to the trajectories by reformulating the problem as the local null controllability of a nonlinear system with distributed controls. Our approach leverages the Lyusternik-Graves theorem to achieve local inversion, leading to the desired controllability result. Finally, we illustrate our theoretical findings through several numerical experiments based on the Physics-Informed Neural Networks (PINNs) approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control of the Fisher-Stefan system Boutaayamou, Idriss Et-tahri, Fouad Maniar, Lahcen Periago, Francisco Optimization and Control This paper addresses the exact controllability of trajectories in the one-dimensional Fisher-Stefan problem--a reaction-diffusion equation that models the spatial propagation of biological, chemical, or physical populations within a free-end domain, governed by Stefan's law. We establish the local exact controllability to the trajectories by reformulating the problem as the local null controllability of a nonlinear system with distributed controls. Our approach leverages the Lyusternik-Graves theorem to achieve local inversion, leading to the desired controllability result. Finally, we illustrate our theoretical findings through several numerical experiments based on the Physics-Informed Neural Networks (PINNs) approach. |
| title | Control of the Fisher-Stefan system |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.23154 |