研究了一类具有尺度结构的线性种群模型的适定性及最优不育控制问题.首先应用Volterra积分方程和Banach不动点原理证明模型解的存在唯一性,并给出解关于控制变量连续依赖性定理;其次应用Mazur定理证明了最优策略的存在性;最后借助法锥和共轭系统导出最优性条件.

This paper is concerned with the well-posedness and optimal contraception control problem for a linear size-structured population model. The existence of a unique non-negative solution is established by using the Banach fixed point theorem. The existence of a unique optimal strategy is derived by Mazur's theorem in convex analysis, and the optimality conditions are derived by means of normal cone and adjoint system.