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 -