| 非线性依赖年龄的人口动态最优收获 |
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| 引用本文： | 李明,姚云飞.非线性依赖年龄的人口动态最优收获[J].阜阳师范学院学报(自然科学版),2006,23(4):61-64. |
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| 作者姓名： | 李明 姚云飞 |
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| 作者单位： | 1. 华中科技大学,数学系,湖北,武汉,430074
2. 阜阳师范学院,数学系,安徽,阜阳,236041 |
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| 摘 要： | 在L1(0,T)空间内研究非线性依赖年龄的人口动态的最优控制问题.通过分离收获项,把该人口发展方程分离成两个便于分析求解的子方程.一个是带有初始条件和边界条件的偏微分方程,另一个是带有初始条件的常微分方程.并且分别详细论证了其解的存在唯一性,从而得到原人口方程解的存在唯一性;最后在人口系统存在解的基础上,用控制收敛定理证明其最优控制的存在性.
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| 关 键 词： | 人口动力系统 Carathe。odory解 最优控制 |
| 文章编号： | 1004-4329（2006）04-0019-04 |
| 收稿时间： | 2006-09-06 |
| 修稿时间： | 2006年9月6日 |
Optimal Harvesting for a Nonlinear Age-Dependent Population Dynamics |
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| LI Ming,YAO Yun-fei.Optimal Harvesting for a Nonlinear Age-Dependent Population Dynamics[J].Journal of Fuyang Teachers College:Natural Science,2006,23(4):61-64. |
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| Authors: | LI Ming YAO Yun-fei |
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| Institution: | 1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan , 430074, China; 2. Department of Mathematics, Fuyang Teachers College, Fuyang 236041, China |
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| Abstract: | We study an optimal controlling problem for a nonlinear age-dependent population dynamics in the space in the letterpress.By dividing the harvesting term,we separate two young equations that are easy to analyse and seek solution from the population dynamics equation.One is the partial differential equation that parentheses the initial condition and the boundary condition,the other is the ordinary differential equation that parenthese the initial condition.The existence and the uniqueness of their solutions are also demonstrated respectively in detail,and accordingly the existence and uniqueness of solution of the former equation are proven;Finally on the base of the existence of the solution,we prove the existence of an optimal control with the control-convergence theory. |
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| Keywords: | population dynamics solution optimal control |
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