Optimal Control of the Obstacle Problem in a Perforated Domain
Optimal Control of the Obstacle Problem in a Perforated Domain
复制标题
穿孔域障碍问题的最优控制
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Martin H. Strömqvist
中科院分区：
文献类型：
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作者：
Martin H. Strömqvist
研究了周期性分布小孔穿孔区域中障碍问题解的最优控制问题。通过选择穿孔障碍物来控制该解决方案，该穿孔障碍物以这样的方式选择，即该解决方案接近给定的轮廓并且该障碍物不是太不规则。我们证明了最优障碍的存在性、唯一性和稳定性，并给出了最优性的充分必要条件。当洞数无限增加时，我们确定了最优障碍和最优解序列的极限。这个极限很大程度上取决于孔的尺寸收缩的速率。
We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink.