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 language | English |
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Pages (from-to) | 677-690 |
Number of pages | 14 |
Journal | Applied Mathematics and Computation |
Volume | 320 |
DOIs | |
Publication status | Published - 1 Mar 2018 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Inc.
Keywords
- Optimization
- Population biology
- Reaction-diffusion
- Rearrangements of functions
- Symmetry
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics