论文标题
最佳控制问题由1-D Kobayashi-Warren-Carter类型系统管理
Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems
论文作者
论文摘要
本文致力于研究由1-D Kobayashi-Warren-Carter型系统控制的一类最佳控制问题，该系统基于[Kobayashi等人，Physica d，140，141-141-150，2000]提出的基于晶界运动的相位模型。该类别由Kobayashi-Warren-Carter类型的物理现实状态系统及其正则化近似问题组成的最佳控制问题。本文的结果在三个主要定理1-3中陈述。第一个主要定理1涉及对状态系统的解决性和连续依赖性。同时，第二个主要定理2与最佳控制问题的最佳控制问题的溶解度有关，在我们的最佳控制问题类别中的某些半连续关联。最后，在第三个主要定理3中，我们得出了第一阶的最佳控制条件，以最佳控制正规化近似问题。通过采用近似限制，我们还得出了用于物理现实问题的最佳控制的最佳条件。
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140, 141-150, 2000]. The class consists of an optimal control problem for a physically realistic state-system of Kobayashi-Warren-Carter type, and its regularized approximating problems. The results of this paper are stated in three Main Theorems 1-3. The first Main Theorem 1 is concerned with the solvability and continuous dependence for the state-systems. Meanwhile, the second Main Theorem 2 is concerned with the solvability of optimal control problems, and some semi-continuous association in the class of our optimal control problems. Finally, in the third Main Theorem 3, we derive the first order necessary optimality conditions for optimal controls of the regularized approximating problems. By taking the approximating limit, we also derive the optimality conditions for the optimal controls for the physically realistic problem.
