论文标题
关于无粘性和粘性汉堡的均匀可控性 - $α$系统
On the Uniform Controllability of the Inviscid and Viscous Burgers-$α$ Systems
论文作者
论文摘要
这项工作致力于证明无粘性和粘性汉堡$α$系统的全球统一确切可控性。状态$ y $是正规汉堡方程的解决方案，其中传输速度$ z $由$ y $的过滤版本组成 - 特别是$ z =（id -α^2 \ partial^partial^2_ {xx}）^{-1} y $，$α> 0 $是$ y $ $ y $的小参数。首先，使用返回方法，获得了具有三个标量控件的非视觉汉堡系统的全局均匀确切可控性结果。然后，从局部精确的可控性结果中推导了粘性系统恒定状态的全局确切可控性，以及平滑初始和目标状态的全局近似可控性结果。
This work is devoted to prove the global uniform exact controllability of the inviscid and viscous Burgers-$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.
