Optimal boundary control problems for a hierarchical age-structured two-species model

This paper discusses the optimal control problems for a nonlinear age-structured two-species model, where elder individuals are more competitive than younger ones, and each species is described by a nonlinear integropartial differential equation with a global feedback boundary condition. First, we establish the existence of a unique nonnegative bounded solution by means of frozen coefficients and the fixed-point theorem. More importantly, we discuss the least deviation-cost problem and the most benefit-cost problem. For the least deviation-cost problem, the existence of an optimal strategy is established by means of Ekeland's variational principle, and the minimum principle is obtained via an adjoint system. Meanwhile, the corresponding results for the most benefit-cost problem are given. In addition, some numerical experiment results are presented to examine the effects of parameters on the optimal policies and indexes.