山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (7): 15-20.doi: 10.6040/j.issn.1671-9352.0.2017.578
曹雪靓,雒志学
CAO Xue-jing, LUO Zhi-xue
摘要： 研究了污染环境下一类森林发展系统的最优控制问题。首先,提出所研究的模型并通过Banach不动点定理证明了解的存在唯一性,然后根据凸泛函的性质以及Mazur引理得出最优控制的唯一解。
中图分类号:
| [1] HALLAM T G, CLARK C E, LASSITER R R. Effects of toxicants on populations: a qualitative approach I. equilibrium environmental exposure[J]. Ecological Modelling, 1983, 18(4): 291-304. [2] HALLAM T G, CLARK C E, JORDAN G S. Effects of toxicants on populations: a qualitative approach II. first order kinetics[J]. Journal of Mathematical Biology, 1983, 18(1): 25-37. [3] HALLAM T G, DE LUNA J T. Effects of toxicants on populations: a qualitative approach III. environmental and food chain pathways[J]. Journal of Theoretical Biology, 1984, 109(3): 411-429. [4] LUO Zhixue, HE Zerong. Optimal control for age-dependent population hybrid system in a polluted environment[J]. Applied Mathematics and Computation, 2014, 228(1): 68-76. [5] LUO Zhixue, FAN Xueliang. Optimal control for an age-dependent competitive species model in a polluted environment[J]. Applied Mathematics and Computation, 2014, 228(1): 91-101. [6] WANG Dingjiang, ZHANG Yufeng. The property of solution of a nonstationary forest evolution system[J]. Systems Science and Systems Engineering, 1993, 2(3): 281-288. [7] 高德智,许香敏.森林发展系统中的最优控制问题[J].系统工程理论与实践, 1999(4): 90-93. GAO Dezhi, XU Xiangmin. Optimal control problems in forest evolution system[J]. Systems Engineering-Theory and Practice, 1999(4): 90-93. [8] 马知恩.种群生态学的数学建模与研究[M].合肥:安徽教育出版社, 1996: 168-175. MA Zhien. Mathematical modeling and research on population ecology[M]. Hefei: Anhui Education Press, 1996: 168-175. [9] HE Zerong, LIU Yan. An optimal birth control problem for a dynamical population model with size-structure[J]. Nonlinear Analysis: Real World Applications, 2012, 13(3): 1369-1378. [10] LIU Yan, CHENG Xiaoliang, HE Zerong. On the optimal harvesting of size-structured population dynamics[J]. Applied Mathematics-A Journal of Chinese Universities, 2013, 28(2): 173-186. [11] ANITA S. Analysis and control of age-dependent population dynamics[M]. Boston: Kluwer Academic, 2000: 67-70. |
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