The Optimal Control For Two Classes Of Nonlinear Age-dependent Population System

As a renewable resources, the population dynamics not only have a direct economic value on people's lives, but also have an extremely important value of ecological environment. Therefore, for the development of population resources, it must be centered on economics and ecological benefit, control the operating factor within renewable power, so as to make population resources be protected and proliferated and then achieve its purpose of sustainable use.Recently people focus on the control problem of time-varing population dynamics with age-dependent and spatial diffusion. On the basis of the functional analysis and the optimal control theories, this paper considers the optimal control for a single population dynamics. According to the contents, this paper is divided into three chapters:In the first chapter, we give the preface. It introduces the background, the present studying of population dynamics at home and abroad and the preparative theories.In the second chapter, the problem of the optimal control for a class of non-linear population dynamics system with age-dependent is discussed. The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland's variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.In the third chapter, it is about the optimal control for a class of nonlinear population system with diffusion. The existence of the optimal control for the system is demonstrated via compactness theorem and prior estimates. Then the necessary conditions of optimal control problem is obtained by the conception of normal cone.