Second-Order Necessary/Sufficient Optimality Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls
Second-Order Necessary/Sufficient Optimality Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls
复制标题
含首项控制的半线性椭圆方程的二阶必要/充分最优性条件
DOI：
10.3934/mcrf.2018003
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发表时间：
2018
影响因子：
1.2
通讯作者：
雍炯敏
中科院分区：
文献类型：
--
作者：
楼红卫;雍炯敏
考虑一类散度型半线性椭圆型方程的最优控制问题。状态方程的首项和半线性项都含有控制项。最优控制的著名的庞特里亚金型最大值原理是最优控制的一阶必要条件。当这样的一阶必要条件在某种意义上是奇异的时，某种类型的二阶必要条件就会自然出现。本文的目的就是探讨最优控制问题的这种条件。
An optimal control problem for a semilinear elliptic equation of.divergence form is considered. Both the leading term and the semilinear term.of the state equation contain the control. The well-known Pontryagin type.maximum principle for the optimal controls is the rst-order necessary condition..When such a rst-order necessary condition is singular in some sense,.certain type of the second-order necessary condition will come in naturally..The aim of this paper is to explore such kind of conditions for our optimal.control problem.