Qiangjun Xie, Ze-Rong He, Xiaohui Wang
Abstract:
In this article, we consider an optimal harvesting control problem for
a spatial diffusion population system, which incorporates
individual's random growth of size and distributed style of recruitment.
The existence and uniqueness of nonnegative solutions to
this practical model is established by means of Banach's fixed point theorem.
The continuous dependence of population density on the
harvesting effort is analyzed. The optimal harvesting strategies are
discussed through normal cone and adjoint techniques.
Some conditions are presented to assure that there is only one optimal policy.
Submitted September 10, 2015. Published August 11, 2016.
Math Subject Classifications: 92B05, 93C20, 49K20.
Key Words: Optimal harvesting; spatial diffusion; size-structured model;
random growth; normal cone.
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Qiangjun Xie Institute of Operational Research and Cybernetics Hangzhou Dianzi University Zhejiang 310018, China email: qjunxie@hdu.edu.cn |
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Ze-Rong He Institute of Operational Research and Cybernetics Hangzhou Dianzi University Zhejiang 310018, China email: zrhe@hdu.edu.cn |
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Xiaohui Wang Department of Mathematics University of Texas-Rio Grande Valley Edinburg, TX 78539, USA email: xiaohui.wang@utrgv.edu |
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