Optimal harvesting strategy based on rearrangements of functions

Emamizadeh, Behrouz and Farjudian, Amin and Liu, Yichen (2018) Optimal harvesting strategy based on rearrangements of functions. Applied Mathematics and Computation, 320 . pp. 677-690. ISSN 0096-3003

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Abstract

We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments.

Item Type: Article
Additional Information: © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Population biology; Rearrangements of functions; Reaction-diffusion; Optimization; Symmetry
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1016/j.amc.2017.10.006
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Depositing User: Yu, Tiffany
Date Deposited: 05 Mar 2019 06:52
Last Modified: 05 Nov 2019 04:30
URI: http://eprints.nottingham.ac.uk/id/eprint/56208

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