摘 要
隨着市場經濟和現代工業的飛速發展，人類面臨了直接危害人類生存的新問題――環境污染。爲了治理污染，提出治理污染的新方案，必須建立合理的數學模型來解決現實問題。
這是1個關於湖泊、河流水質污染處理的數學模型，透過模型的建立與問題解決，能夠較準確地分析並解決實際生活中的水質污染問題。如何合理地解決湖泊、河流污染問題是1個非常切合實際的問題，本問題是目前1個熱門的'研究課題。把此模型看成是1個單流入、單流出的系統，流入、流出的水流速度相同。利用質量守恆定律可列出關於濃度變化的微分方程，透過求解此微分方程可得到模型所要求的某1時刻污染物的濃度。本模型較好地解決了湖水污染處理問題，具有1定的經濟效用和價值，能比較恰當地解決實際問題。
透過對問題的分析，得出湖水污染濃度的變化的結果。在模型建設中採用了比較理想的求解方法，在實際中還是比較有指導意義的。
關鍵詞 微分方程；質量守恆定律；污染濃度
Abstract
Along with the market economy and the present industry rapid development, the new question of the humanity facing - environmental pollution has directly harmed the human survival. In order to control the pollution and propose a new plan, we have to establish the reasonable model to solve the realistic problem.
This is a mathematical model about processing water pollution of the lake and the rivers. Through the establishment of the mathematical model and the solution of the question, we can accurately analyze and solve the question of water pollution in practical life. This question is an extremely realistic question, how to reasonably solve the question of contamination about the lake and the rivers is a lively researched topic today. We regard as this model as the system with a sole entrance and a sole exportation. And the velocity of the inflow and the outflow are same. Using the law of conservation about the changing density we can list a differential equation, through solving this differential equation we can obtain a certain time pollutant density which the model requests . This model has solved the problem well, and it has certain economic utility and value. The model can quite appropriately solve the actual problem.
Through the analysis of the question, we can obtain the result of changing concentration of the contaminant. We have used the quite ideal solution method in the construction of model, and the model has a certain guiding sense in practice.
Key words Differential equation; Law of conservation of mass; Concentration of contaminant
