Cost of controllability of the Burgers' equation linearized at a steady shock in the vanishing viscosity limit
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911520461422592 |
|---|---|
| author | Laheurte, Vincent |
| author_facet | Laheurte, Vincent |
| contents | We consider the one-dimensional Burgers' equation linearized at a stationary shock, and investigate its null-controllability cost with a control at the left endpoint. We give an upper and a lower bound on the control time required for this cost to remain bounded in the vanishing viscosity limit, and construct an admissible control with an explicit limit behavior. We also provide an extension of the analysis to the case where the control acts on both endpoints. The proof relies on complex analysis and adapts methods previously used to tackle the same issue with a constant transport term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cost of controllability of the Burgers' equation linearized at a steady shock in the vanishing viscosity limit Laheurte, Vincent Analysis of PDEs Mathematical Physics 93B05, 93B60, 35B25, 35F05, 35K10 We consider the one-dimensional Burgers' equation linearized at a stationary shock, and investigate its null-controllability cost with a control at the left endpoint. We give an upper and a lower bound on the control time required for this cost to remain bounded in the vanishing viscosity limit, and construct an admissible control with an explicit limit behavior. We also provide an extension of the analysis to the case where the control acts on both endpoints. The proof relies on complex analysis and adapts methods previously used to tackle the same issue with a constant transport term. |
| title | Cost of controllability of the Burgers' equation linearized at a steady shock in the vanishing viscosity limit |
| topic | Analysis of PDEs Mathematical Physics 93B05, 93B60, 35B25, 35F05, 35K10 |
| url | https://arxiv.org/abs/2411.12267 |