Geodesic
Theory of optimal harvesting for a size structured model of fish
Rong Liu1 ; Guirong Liu1
1 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China.
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 1

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This paper investigates the maximum principle for a nonlinear size structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. First, we show the existence of a unique non-negative solution of the system, and give a comparison principle. Next, we prove the existence of optimal policies by using maximizing sequence and Mazur’s theorem in convex analysis. Then, we obtain necessary optimality conditions by using tangent-normal cones and adjoint system techniques. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.
DOI : 10.1051/mmnp/2019006

Rong Liu 1 ; Guirong Liu 1

1 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China. 
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Rong Liu; Guirong Liu. Theory of optimal harvesting for a size structured model of fish. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 1. doi: 10.1051/mmnp/2019006

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