Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2006.05335 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- This work is devoted to prove the global uniform exact controllability of the inviscid and viscous Burgers-$α$ systems. The state $y$ is the solution to a regularized Burgers equation, where the transport velocity $z$ consists of a filtered version of $y$ - specifically $z=(Id-α^2\partial^2_ {xx})^{-1}y$ with $α>0$ being a small parameter - in place of $y$. First, a global uniform exact controllability result for the nonviscous Burgers-$α$ system with three scalar controls is obtained, using the return method. Then, global exact controllability to constant states of the viscous system is deduced from a local exact controllability result and a global approximate controllability result for smooth initial and target states.