On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916820239253504 |
|---|---|
| author | Duca, Alessandro Pozzoli, Eugenio Urbani, Cristina |
| author_facet | Duca, Alessandro Pozzoli, Eugenio Urbani, Cristina |
| contents | In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show the small-time approximate controllability between states sharing the same sign. Moreover, in the one-dimensional case $d=1$, we combine this property with a local exact controllability result, and prove the small-time exact controllability of any positive states towards the ground state of the evolution operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories Duca, Alessandro Pozzoli, Eugenio Urbani, Cristina Analysis of PDEs Optimization and Control 93B05, 35Q93, 35K05 In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show the small-time approximate controllability between states sharing the same sign. Moreover, in the one-dimensional case $d=1$, we combine this property with a local exact controllability result, and prove the small-time exact controllability of any positive states towards the ground state of the evolution operator. |
| title | On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories |
| topic | Analysis of PDEs Optimization and Control 93B05, 35Q93, 35K05 |
| url | https://arxiv.org/abs/2407.10521 |