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Controllability and Stabilizability of a Higher Order Wave Equation on a Periodic Domain
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-04-23 , DOI: 10.1137/19m1240472
Shenghao Li , Min Chen , Bingyu Zhang

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:

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 $。
更新日期:2020-04-23
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