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### 具有年龄结构非线性扩散系统的最优控制

1. 兰州交通大学数理学院, 甘肃 兰州 730070
• 收稿日期:2016-01-11 出版日期:2016-05-20 发布日期:2016-05-16
• 作者简介:刘江璧(1990— ), 男, 硕士研究生, 研究方向为生物数学及最优控制理论. E-mail:liujiangbi_2011@163. com
• 基金资助:
国家自然科学基金资助项目(11561041);甘肃省自然科学基金资助项目(1506RJZA071)

### Optimal control for a nonlinear diffusion system with age-dependent

LIU Jiang-bi, LUO Zhi-xue

1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
• Received:2016-01-11 Online:2016-05-20 Published:2016-05-16

Abstract: In this paper, we investigate the optimal harvesting for a class of nonlinear diffusion problem in an age-dependent population system with fertility and mortality depending on the population size. Making the maximum revenue from harvested by control the proportion of the species harvested. Mazurs theory is used to obtain existence of an optimal control. Optimality conditions are derived by means of normal cone technique. Some results in references are extended.

• O157.1
 [1] GURTIN M E. A system of equations for age-dependent population diffusion[J]. Thero Biol, 1973, 40(2):389-392.[2] ANITA S. Analysis and control of age-dependent population dynamics[M]. Boston: Kluwer Academic, 2000.[3] 雒志学,李沐春. 具有扩散和年龄结构种群动力系统的最优控制[J].工程数学学报, 2006, 23(4):641-646. LUO Zhixue, LI Muchun. Optimal control for linear population dynamics with age-dependence spatial structure and diffusion[J]. Chinese Journal of Engineering Mathematics, 2006, 23(4):641-646.[4] 吴秀兰, 付军. 具有年龄结构和空间扩散的捕食与被捕食种群系统的最优控制[J].吉林大学学报(理学版), 2010, 48(4):545-550. WU Xiulan, FU Jun. Optimal control for age-dependent predator-prey population dynamics with diffusion[J]. Journal of Jilin University(Science Edition), 2010, 48(4):545-550.[5] BUSENBER S, IANNELLI M. A class of nonlinear diffusion problems in age-dependent population dynamics[J]. Nonlin Anal, 1983 7(5):501-529.[6] AINSEBA B E. Optimal control for a nonlinear age-structured population dynamics model[J]. Electronic Journal of Differential Equations, 2003, 23(28):1-9.[7] ZHAO Chun, WANG Miansen, ZHAO Ping. Optimal harvesting problems for age-dependent interacting species with diffusion[J]. Comput Math Appl, 2005, 163(1):117-129.[8] BARBU V, IANNELLI M. Optimal control of population dynamics[J]. Optim Theory Appl, 1999, 102(1):1-14.[9] BARBU V. Mathematical methods in Optimization of differential systems[M]. Dordrecht: Kluwer Academic Publishers, 1994.
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