Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow
Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow
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DOI：
10.3934/dcds.2016036
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发表时间：
2016-07
影响因子：
1.1
通讯作者：
Chang-jie Fang;W. Han
中科院分区：
文献类型：
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作者：
Chang-jie Fang;W. Han
利用克拉克亚微分描述的非线性边界条件研究了瞬态斯托克斯流体流动问题。我们提出了该问题的等价弱表述，其中之一采用半变分不等式的形式。解的存在性通过基于时间半离散近似的限制过程来显示。解决方案的独特性及其对数据的持续依赖也已确定。最后，我们提出了半变分不等式最优控制问题解的存在性的结果。
A time-dependent Stokes fluid flow problem is studied with nonlinear boundary conditions described by the Clarke subdifferential. We present equivalent weak formulations of the problem, one of them in the form of a hemivariational inequality. The existence of a solution is shown through a limiting procedure based on temporally semi-discrete approximations. Uniqueness of the solution and its continuous dependence on data are also established. Finally, we present a result on the existence of a solution to an optimal control problem for the hemivariational inequality.