一类带齐次分裂核的群体平衡方程的相似分析及相似解  

The Similarity Analysis and Solutions of a Class of Population Balance Equations with Homogeneous Fragmentation Kernels

作　　者：林府标 王骞 张千宏 LIN Fubiao;WANG Qian;ZHANG Qianhong(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang Guizhou 550025,China;The Middle School Attached to the Guizhou Normal University,Guiyang Guizhou 550001,China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025 [2]贵州师范大学附属中学,贵州贵阳550001

出　　处：《江西师范大学学报（自然科学版）》2022年第2期215-220,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11761018,11361012);贵州省科技计划基金(黔科合基础-ZK[2022]一般021);贵州省科技厅科学技术基金([2020]1Y008);贵州省教育厅创新群体(黔教合KY字[2021]015)资助项目.

摘　　要：该文研究一类带齐次分裂核的群体平衡方程的相似分析及相似解.首先将尺度变换群法用于一类带齐次分裂核的群体平衡方程,探寻尺度函数的相似不变量,用自相似不变量构造自相似解;其次用解的群变换和自相似解获得了原方程的相似解、显式精确解、约化方程,分析了解的动力学性态;最后,相似分析结果表明:尺度变换群法不仅可用于纯微分方程,而且可用于群体平衡方程.The similarity analysis and solutions of a class of population balance equations with homogeneous fragmentation kernels are studied in this paper.Firstly,the method of scaling transformation group is applied to a class of population balance equations with homogeneous fragmentation kernels to explore the similarity invariant variables of scaling functions.The self-similar solutions are constructed by the self-similar invariant variables.Secondly,the similarity solutions,exact explicit solutions and reduced integro-ordinary differential equations of the original equations are obtained by using group transformation of solutions and self-similar solutions.The analysis of dynamic behavior of solution is also presented.Finally,the similarity analysis results show that the scaling transformation group can not only be used for pure differential equations,but also be applied to population balance equations.

关 键 词：群体平衡方程 尺度变换群 相似不变量 相似解 

分 类 号：O175.5[理学—数学] O175.6[理学—基础数学]