| Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives |
| |
| 引用本文： | Shang Wei ZHU. Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives[J]. 数学学报(英文版), 2006, 22(2): 607-624. DOI: 10.1007/s10114-005-0688-0 |
| |
| 作者姓名： | Shang Wei ZHU |
| |
| 作者单位： | [1]Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China [2]Department of Applied Mathematics, Shanxi Finance ~= Economics University, Taiyuan 030006, P. R. China |
| |
| 基金项目： | This work is partially supported by the Chinese NSF under grant 101310310, the NSF under grant 10171059, the NSF under grant 10171030 the National Distinguished Youth Science Foundation of China under grant 10325101, and the Chinese Education Ministry Science Foundation under grant 20030246004. The author would like to thank the late Professor Xunjing Li for his encouragement, and thank Professors Shanjian Tang, Xu Zhang and Liping Pan for their invaluable and critical suggestions. |
| |
| 摘 要： |
|
| 关 键 词： | 最优化控制 变化不等式 时滞算子 导数 |
| 收稿时间： | 2004-09-29 |
| 修稿时间： | 2004-09-292004-11-11 |
Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives |
| |
| Shang Wei Zhu. Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives[J]. Acta Mathematica Sinica(English Series), 2006, 22(2): 607-624. DOI: 10.1007/s10114-005-0688-0 |
| |
| Authors: | Shang Wei Zhu |
| |
| Affiliation: | (1) Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China;(2) Department of Applied Matematics, Shanxi Finance & Economics University, Taiyuan 030006, P. R. China |
| |
| Abstract: | In this paper, an optimal control problem for parabolic variational inequalities with delays in the highest order spatial derivatives is investigated. The well-posedness of such kinds of variational inequalities is established. The existence of optimal controls under a Cesari-type condition is proved, and the necessary conditions of Pontryagin type for optimal controls is derived. |
| |
| Keywords: | Variational inequalities Time-delay operator Optimal control. Maximum Drinciple |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
