Observability from measurable sets for a parabolic equation involving the Grushin operator and applications
Observability from measurable sets for a parabolic equation involving the Grushin operator and applications
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DOI：
10.1002/mma.4266
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发表时间：
2017-07
影响因子：
2.9
通讯作者：
Hanbing Liu;Can Zhang
中科院分区：
文献类型：
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作者：
Hanbing Liu;Can Zhang
本文利用已有的实解析函数可测集上的Carleman估计和传播估计，结合伸缩级数方法，建立了具有Grushin算子的抛物方程在时空变量上的可测集上的可观测不等式。对于这类奇异抛物型方程的时间最优控制问题和范数最优控制问题，我们可以应用这个可观测性不等式来证明它的邦邦性质。版权所有©2016 John Wiley & Sons， Ltd。
In this work, we utilize the existing Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, together with the telescoping series method, to establish an observability inequality from measurable subsets in time‐space variable for the parabolic equation with Grushin operator in some multidimension domains. We can apply this observability inequality to show the bang–bang property for both time optimal and norm optimal control problems for this kind of singular parabolic equation. Copyright © 2016 John Wiley & Sons, Ltd.