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Optimal harvesting strategy based on rearrangements of functions

Author

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  • Emamizadeh, Behrouz
  • Farjudian, Amin
  • Liu, Yichen

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.

Suggested Citation

  • Emamizadeh, Behrouz & Farjudian, Amin & Liu, Yichen, 2018. "Optimal harvesting strategy based on rearrangements of functions," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 677-690.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:677-690
    DOI: 10.1016/j.amc.2017.10.006
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    Cited by:

    1. K. D. Searle & J. H. Vuuren, 2022. "A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-19, December.
    2. Searle, K.D. & van Vuuren, J.H., 2021. "An abstract mathematical model for sustainable harvesting of a biological species on the boundary of a protected habitat," Ecological Modelling, Elsevier, vol. 452(C).

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