多区域碳排放跨界污染问题研究  

Research of Multi-area Carbon Emission Transboundary Pollution Problems

作　　者：鲁祖亮[1,2] 王干湘[3] 杨雨倩 刘豪 刘小雨 LU Zu-liang;WANG Gan-xiang;YANG Yu-qian;LIU Hao;LIU Xiao-yu(Key Laboratory for Nonlinear Science and System Structure,Reaserch Center of Substainable Development in Three Gorges Reservoir Area,Chongqing Three Gorges University,Chongqing 404020,China;Research Center for Mathematics and Economics,Tianjin University of Finance and Economics,Tianjin 300222,China;Hunan International Economics University,Business College,Changsha 410205,China)

机构地区：[1]重庆三峡学院非线性科学与系统结构重点实验室,三峡库区可持续发展研究中心,重庆404020 [2]天津财经大学数学与经济研究中心,天津300222 [3]湖南涉外经济学院商学院,湖南长沙410205

出　　处：《数学的实践与认识》2020年第22期1-10,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201510);重庆市高校科研创新团队(CXTDX201601035);中国博士后科学基金(2017T100155,2015M580197);三峡库区可持续发展研究中心科学研究项目(2019sxxyjd07);重庆市科委项目(cstc2019jcyj-msxmX0280)。

摘　　要：利用自适应共振理论对多区域跨界污染的相似度进行分类,提出跨界工业污染问题和碳排放交易条件下的随机微分博弈模型,利用随机最优控制理论推导出合作博弈模型的哈密顿-雅可比-贝尔曼方程,应用拟合有限体积法来求解该方程,并利用数值算例验证了算法的实用性和有效性。In this paper,adaptive resonance theory was used to classify the similarity of multiarea transboundary pollution.We give a stochastic differential game to model the transboundary industrial pollution problems with carbon emission permits trading.We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman equations for the cooperative games,and then propose a fitted finite volume method to solve it.The efficiency and the usefulness of this method are illustrated by an empirical study.

关 键 词：跨界污染问题 随机微分博弈模型 哈密顿-雅可比-贝尔曼方程 隐式有限差分法 拟合有限体积法 

分 类 号：X321[环境科学与工程—环境工程]