Abstract:

The authors discussed the optimal boundary control for a semilinear age dependent population system based on weight, proved the existence of optimal boundary control via Mazur’s theorem. We obtained the necessary conditions for an optimal control, using Gteax differentiation and Lions’ theory of variational inequalities; and then obtained the optimality system consisting of integral paritial differential equation and variational inequalities. The optimality system can determine optimal control. These results may serve as theoretical reference for practical researches of the control problem in population systems. Its optimality systems determine the optimal control.

Key words:  populationweighted system, optimal boundary control, firstorder necessary condition, optimality system