Optimal harvesting strategy based on rearrangements of functions

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4 Citations (Scopus)
1 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)677-690
Number of pages14
JournalApplied Mathematics and Computation
Volume320
DOIs
Publication statusPublished - 1 Mar 2018

Keywords

  • Optimization
  • Population biology
  • Reaction-diffusion
  • Rearrangements of functions
  • Symmetry

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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