We consider a nonlinear profit maximization problem in the Lotka–McKendrick model of age-structured harvested population describing farmed populations in agriculture and aquaculture. The control functions are time- and age-dependent harvesting rate and time dependent supply of newborns. We establish the existence of optimal controls with measure-valued harvesting rate by using distributional partial derivatives of functions of bounded variation through the equivalent integrated form to the original problem.

中文翻译：

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年龄结构人口最优控制中测值解的存在性

我们考虑 Lotka-McKendrick 模型中的非线性利润最大化问题，该模型描述了农业和水产养殖中养殖人口的年龄结构收获人口。控制功能是依赖于时间和年龄的采集率和依赖于时间的新生儿供应。我们通过对原始问题的等效积分形式，使用有界变分函数的分布偏导数，建立了具有测值收获率的最优控制的存在性。