| 具年龄和加权的半线性种群系统的最优边界控制 |
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| 引用本文： | 付军,朱宏.具年龄和加权的半线性种群系统的最优边界控制[J].吉林大学学报(理学版),2013,51(1):27-33. |
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| 作者姓名： | 付军 朱宏 |
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| 作者单位： | 1. 吉林师范大学 数学学院, 吉林 四平 136000； 2. 吉林师范大学 计算机学院, 吉林 四平 136000 |
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| 基金项目： | 吉林省自然科学基金(批准号:201115222);吉林师范大学研究生创新项目(批准号:201114) |
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| 摘 要： | 讨论一类具年龄和加权的半线性种群系统的最优控制问题. 运用Mazur’s定理证明了最优边界控制的存在性, 利用Gteax微分和Lions的变分不等式理论得到了控制为最优的一阶必要条件, 从而得到了由积分偏微分方程和变分不等式构成的最优性组, 该最优性组能确定最优控制.
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| 关 键 词： | 加权种群系统 最优边界控制 一阶必要条件 最优性组 |
| 收稿时间： | 2012-05-25 |
Optimal Boundary Control for a Semi-linear Age-Dependent Population System Based on Weight |
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| FU Jun,ZHU Hong.Optimal Boundary Control for a Semi-linear Age-Dependent Population System Based on Weight[J].Journal of Jilin University: Sci Ed,2013,51(1):27-33. |
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| Authors: | FU Jun ZHU Hong |
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| Institution: | 1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;
2. College of Computer, Jilin Normal University, Siping 136000, Jilin Province, China |
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| Abstract: | The authors discussed the optimal boundary control for a semi linear age dependent population system based on weight, proved the existence of optimal boundary control via Mazur’s theorem. We obtained the necessaryconditions for an optimal control, using Gteax differentiation and Lions’ theory of variational inequalities; and then obtained the optimalitysystem consisting of integral paritial differential equation and variational inequalities. The optimality system can determine optimal control. These results may serve as theoretical reference for practical researches of the control problem in population systems. Its optimality systems determine the optimalcontrol. |
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| Keywords: | population weighted system optimal boundary control first order necessary condition optimality system |
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