The bang-bang property of time and norm optimal control problems for parabolic equations with time-varing fractional Laplacian
The bang-bang property of time and norm optimal control problems for parabolic equations with time-varing fractional Laplacian
复制标题
时变分数拉普拉斯抛物型方程的时间bang-bang性质与范数最优控制问题
DOI：
10.1051/cocv/2017075
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Zhang Liang
中科院分区：
文献类型：
--
作者：
Yu Xin;Zhang Liang
本文研究了在有界区域上发展的时变分数阶Laplacian控制的抛物型方程的时间和范数最优控制问题的bang-bang性质。首先得到了一类由时变分数阶Laplacian控制的抛物型方程在某一时刻的唯一的定量延拓。然后，我们建立了上述方程的解的时间可测集的可观测性不等式。最后，借助于能观性不等式，得到了时间和范数最优控制问题的bang-bang性质。
In this paper, we establish the bang-bang property of time and norm optimal control problems for parabolic equations governed by time-varying fractional Laplacian, evolved in a bounded domain of ℝd. We firstly get a quantitative unique continuation at one point in time for parabolic equations governed by time-varying fractional Laplacian. Then, we establish an observability inequality from measurable sets in time for solutions of the above-mentioned equations. Finally, with the aid of the observability inequality, the bang-bang property of time and norm optimal control problems can be obtained.