| 一类种群系统的适定性及最优收获问题 |
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| 引用本文： | 赵春,王绵森,赵平.一类种群系统的适定性及最优收获问题[J].系统科学与数学,2005,25(1):001-012. |
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| 作者姓名： | 赵春 王绵森 赵平 |
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| 作者单位： | 1. 西安交通大学理学院,西安,710049
2. 西安交通大学电信学院,西安,710049 |
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| 基金项目： | 国家自然科学基金(10161009)资助课题 |
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| 摘 要： | 本文研究了一类非线性时变种群扩散系统的适定性及最优收获问题.利用压缩不 动点原理讨论了该种群系统的解的存在唯一性.证明了最优收获控制的存在性,并且获 得了最优控制的唯一性和所满足的必要条件.
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| 关 键 词： | 最优收获 种群系统 适定性 极值原理 |
| 修稿时间： | 2003年11月3日 |
THE WELL POSEDNESS AND THE OPTIMAL HARVESTING PROBLEM FOR A CLASS OF POPULATION DYNAMICS |
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| Zhao Chun,Wang Miansen,Zhao Ping.THE WELL POSEDNESS AND THE OPTIMAL HARVESTING PROBLEM FOR A CLASS OF POPULATION DYNAMICS[J].Journal of Systems Science and Mathematical Sciences,2005,25(1):001-012. |
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| Authors: | Zhao Chun Wang Miansen Zhao Ping |
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| Institution: | (1)School of Science, Xi'an Jiaotong University;(2)School of Electronic and Information Engineering,Xi'an Jiaotong University |
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| Abstract: | In this paper, we investigate the well posedness and the optimal harvesting problem for a class of nonlinear time-dependent population system with diffusion. Both existence and uniqueness of a positive solution are proven using the fixed point theorem. Existence of the optimal harvesting rate control is given, and the necessary condition for optimality and the uniqueness of the optimal control is obtained. |
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| Keywords: | Optimal harvesting population dynamics well-posedness the maximum principle |
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