一类群体平衡方程的伸缩变换群分析及自相似解  

Analysis of scaling transformation group and self-similar solutions of a class of population balance equation

作　　者：林府标 张千宏 LIN Fubiao;ZHANG Qianhong(School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025

出　　处：《安徽大学学报（自然科学版）》2020年第3期6-12,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11761018,11361012);贵州省科技计划基金资助项目(黔科合基础[2019]1051);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]150);2018年度贵州财经大学校级科研基金资助项目(2018XYB04);贵州财经大学创新探索及学术新苗项目(黔科合平台人才[2017]5736-020)。

摘　　要：首先分析和探究带有增长、聚合和破损过程的群体平衡方程;其次把伸缩变换群法用于群体平衡方程,获得群体平衡方程所接受的伸缩变换群、自相似解、精确解和约化的常微分-积分方程;最后所获得结果表明伸缩变换群法不但可用于偏微分方程而且可用于偏微分-积分方程.Firstly,a class of population balance equation involving growth process,aggregation process and breakage process was investigated and analyzed.Secondly,the method of scaling transformation group was applied to this population balance equation.Thirdly,the admitted scaling group,self-similar solutions and reduced equations of this population balance equation were obtained.Finally,these obtained results showed that the method of scaling transformation group could be used not only for partial differential equations but also for integro-differential equations.

关 键 词：群体平衡方程 伸缩变换群法 自相似解 

分 类 号：O175.5[理学—数学]