Math. Model. Nat. Phenom.
Volume 15, 2020
Ecology and evolution
|Number of page(s)||15|
|Published online||24 January 2020|
Theory of optimal harvesting for a size structured model of fish
School of Mathematical Sciences, Shanxi University,
Shanxi 030006, PR China.
* Corresponding author: email@example.com
Accepted: 24 January 2019
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.
Mathematics Subject Classification: 49K20 / 92D25 / 35F50
Key words: Size-structure / maximum principle / adjoint system / normal cone
© EDP Sciences, 2020
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