Global boundary stabilization of 1d systems of scalar conservation laws
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915919103524864 |
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| author | Bastin, Georges Coron, Jean-Michel Hayat, Amaury |
| author_facet | Bastin, Georges Coron, Jean-Michel Hayat, Amaury |
| contents | We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of $L^{\infty}$ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in the $L^1$ and $L^\infty$ norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global boundary stabilization of 1d systems of scalar conservation laws Bastin, Georges Coron, Jean-Michel Hayat, Amaury Analysis of PDEs Systems and Control Optimization and Control 35B40, 35L40, 35L50, 35L65, 93D23, 93D30 We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of $L^{\infty}$ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in the $L^1$ and $L^\infty$ norms. |
| title | Global boundary stabilization of 1d systems of scalar conservation laws |
| topic | Analysis of PDEs Systems and Control Optimization and Control 35B40, 35L40, 35L50, 35L65, 93D23, 93D30 |
| url | https://arxiv.org/abs/2604.05054 |