Electron. J. Diff. Equ., Vol. 2016 (2016), No. 214, pp. 1-13.

Optimal harvesting in diffusive population models with size random growth and distributed recruitment

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
Ze-Rong He
Institute of Operational Research and Cybernetics
Hangzhou Dianzi University
Zhejiang 310018, China
email: zrhe@hdu.edu.cn
Xiaohui Wang
Department of Mathematics
University of Texas-Rio Grande Valley
Edinburg, TX 78539, USA
email: xiaohui.wang@utrgv.edu

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