Maximum principle for a nonlinear size-structured model of fish and fry management - Liu, Rong; Liu, Guirong (Nonlinear Analysis: Modelling and Control, 2018)
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. We establish the well-posedness of the state system by Banach fixed-point theorem. Necessary conditions for optimality are established via the normal cone technique and adjoint system. The existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point reasoning. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.
Keywords: size-structure; maximum principle; well-posedness; uniqueness; Ekeland's variational principle