Emission Control And Treatment Of Shallow Lake System

In this paper,a shallow lake that is potentially subject to eutrophication by excess phosphorous(P)loading is studied.Human activities destroy the phosphorus cycle of the lake.Even under a lower phosphorus input,the lake can not come back to the clear state by its own sinking,that is when the treatment is necessary.The chemical precipitation method is chosen to separate the phosphorus from the water body.The government or a regulatory agency,as the decision maker,needs to co-ordinate the benefits of polluters and lake users,determine the amount of phosphorus input and the ratio of treatment,and at the same time bear the costs of treatment.Treatment costs are composed of a start-up cost and unit costs,and the start-up cost is introduced into the utility function in the form of a indicator function.In the model part,the Hamilton system is established to obtain that the treatment is always carried out in the maximum proportion.After that,the HJB equation is established and the numerical experiment is carried out.Through the discussion of technical parameters:the start-up cost γand the maximum treatment ratio A,it can be concluded that the treatment can always bring higher economic benefits.When the technical level is relatively high(the start-up cost y is small,the maximum treatment ratio A is large),the treatment can change the equilibrium state of the lake to form a long-term treatment mechanism.