TY - JOUR

T1 - Optimal harvesting strategy based on rearrangements of functions

AU - Emamizadeh, Behrouz

AU - Farjudian, Amin

AU - Liu, Yichen

N1 - Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Optimization

KW - Population biology

KW - Reaction-diffusion

KW - Rearrangements of functions

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=85032664267&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2017.10.006

DO - 10.1016/j.amc.2017.10.006

M3 - Article

AN - SCOPUS:85032664267

SN - 0096-3003

VL - 320

SP - 677

EP - 690

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -