研究一类具有个体尺度结构的非线性种群控制模型.确立了状态系统模型非负解的存在唯一性,以及状态关于控制变量的连续依赖性.应用紧性推理和极值化序列法证明了最优策略的存在性,借助切锥法锥和共轭系统技巧导出了最优性条件.

We study an optimal harvesting problem for a nonlinear size-structured popu-lation model. The existence of a unique non-negative solution is established, and the continuousdependence of the population density on the harvesting effort is shown. The existence of an op-timal strategy is proved via compactness and extremal sequence, and the optimality conditions are derived by means of normal cone and adjoint system.