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Optimal Harvesting of a Size-structured Predator-prey Model

~1Liu Yan ~2He Zerong (1 Department of Mathematics,Zhejiang University,Hangzhou 310027; 2 Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)  
This work is concerned with an optimal harvesting problem for a predator-prey model,in which the prey population is described by a first order partial differential equation (PDE) in a density function and the predator by an ordinary differential equation in total size. The existence and uniqueness of solutions to the state system and the dual system is proven via fixed point theorem.Necessary optimality conditions of first order are established by use of tangent-normal cones and dual system technique.The existence of a unique optimal control pair is derived by means of Ekeland's variational principle.The resulting conclusion extends some existing results involving age-dependent populations.
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