On optimal boundary control of Ericksen–Leslie system in dimension two
On optimal boundary control of Ericksen–Leslie system in dimension two
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DOI：
10.1007/s00526-019-1676-z
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发表时间：
2018-11
影响因子：
2.1
通讯作者：
Qiao Liu;Changyou Wang;Xiaotao Zhang;Jianfeng Zhou
中科院分区：
文献类型：
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作者：
Qiao Liu;Changyou Wang;Xiaotao Zhang;Jianfeng Zhou
本文考虑二维简化的Ericksen-Leslie系统的边值问题，其中速度场为无滑移边界条件，单位长度的指向场为含时边界条件。对于这类系统，我们首先证明了在奇性次数有限的情况下整体弱解的存在性，然后在边界数据的像包含在半球内的假设下，证明了唯一的整体强解的存在性。最后，我们将这些定理应用于简化的Ericksen-Leslie系统的最优边界控制问题，证明了最优边界控制的存在性和必要条件。
In this paper, we consider the boundary value problem of a simplified Ericksen–Leslie system in dimension two with non-slip boundary condition for the velocity fielduand time-dependent boundary condition for the director fielddof unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth forunder the assumption that the image of boundary data is contained in the hemisphere. Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen–Leslie system and show both the existence and a necessary condition of an optimal boundary control.