Classical Solutions Of Two Dimension Bamboo Forest Development System

This paper is divided into four parts.Chapter1is devoted to the introduction of the background of this research. We specify some results on various kinds of models of forest ecological system that appeared in literature. In chapter2, by using the method of drawing characteristic-line and the Fixed-point Theorem, we prove the existence and uniqueness of the solutions of the following system model on the age structure of nonlinear plantation about the bamboo forest development system.The above model describes the development process of age density structure of a kind of bamboo forest plantation. The difference between this model and the forest model is that in this model, taking into account the fact that bamboo shoots need not be planted as well the fact that the values of bamboo and bamboo shoots are different, we can maximize the economic benefit by controlling the appropriate retention rate and cutting rate of bamboo shoots.The main conclusions of this section are as follows.(OP1):For any given effective retention rateβ(·) and the cutting rate μ(x, y,t) of the bamboo shoots, the solution p(x, y,t) of the forest system exists and is unique.(OP2):Suppose that p0∈O1[O,l]), β(·)∈O1(R+) and P0(x)>0for all x[O,l]. Then N(t)≥N0for any positive number N0given in advance.Chapter3is a continuation of chapter2. In this chapter, we take into account another factor, i.e. environmental influential factor. With the same method as that in the second chapter, we proved the existence and the uniqueness of the solution of the following model. In the last chapter, we use the maximal sequence to investigate the problem ofcontrolling the optimal retention rate of bamboo shoots which can maximize theeconomic benefit in a operating cycle of the bamboo forest of the following model.Moreover, we investigate the necessary conditions for the optimal solution of theproblem of controlling the optimal cutting rate (x,y,t)of the following model.