SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 1121-1143, January 2020.
This article studies internal control of the sixth order Boussinesq equation $u_{tt}-u_{xx}+\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f $ posed on a periodic domain $\mathbb{T}$ with the internal control input $f(\cdot,t)$ acting on an arbitrarily small open subset of the domain $\mathbb{T}$. It is shown that the system is locally exactly controllable and exponentially stabilizable in the classic Sobolev space $H^{s+3}(\mathbb{T})\times H^s(\mathbb{T})$ for any $s\geq 0$.

中文翻译：

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周期域上高阶波动方程的可控性和可镇定性

SIAM控制与优化杂志，第58卷，第2期，第1121-1143页，2020年1月。
本文研究了六阶Boussinesq方程$ u_ {tt} -u_ {xx} + \ beta u_ {xxxx}-的内部控制u_ {xxxxxx} +（u ^ 2）_ {xx} = f $置于周期域$ \ mathbb {T} $上，内部控制输入$ f（\ cdot，t）$作用于任意小的开放子集$ \ mathbb {T} $的域 结果表明，对于任何$ s，该系统在经典Sobolev空间$ H ^ {s + 3}（\ mathbb {T}）\ times H ^ s（\ mathbb {T}）$中是局部精确可控的，并且是指数稳定的\ geq 0 $。