Feedback stabilization for entropy solutions of a 2x2 hyperbolic system of conservation laws at a junction
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866929443990142976 |
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| author | Coclite, Giuseppe Maria De Nitti, Nicola Garavello, Mauro Marcellini, Francesca |
| author_facet | Coclite, Giuseppe Maria De Nitti, Nicola Garavello, Mauro Marcellini, Francesca |
| contents | We consider the p-system in Eulerian coordinates on a star-shaped network. Under suitable transmission conditions at the junction and dissipative boundary conditions in the exterior vertices, we show that the entropy solutions of the system are exponentially stabilizable. Our proof extends the strategy by Coron et al. (2017) and is based on a front-tracking algorithm used to construct approximate piecewise constant solutions whose BV norms are controlled through a suitable exponentially-weighted Glimm-type Lyapunov functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feedback stabilization for entropy solutions of a 2x2 hyperbolic system of conservation laws at a junction Coclite, Giuseppe Maria De Nitti, Nicola Garavello, Mauro Marcellini, Francesca Analysis of PDEs 35L65, 35L45, 35B25 We consider the p-system in Eulerian coordinates on a star-shaped network. Under suitable transmission conditions at the junction and dissipative boundary conditions in the exterior vertices, we show that the entropy solutions of the system are exponentially stabilizable. Our proof extends the strategy by Coron et al. (2017) and is based on a front-tracking algorithm used to construct approximate piecewise constant solutions whose BV norms are controlled through a suitable exponentially-weighted Glimm-type Lyapunov functional. |
| title | Feedback stabilization for entropy solutions of a 2x2 hyperbolic system of conservation laws at a junction |
| topic | Analysis of PDEs 35L65, 35L45, 35B25 |
| url | https://arxiv.org/abs/2407.21137 |