两类破碎群体平衡方程接受的李群及群不变解  

Admitted Lie Groups and Group Invariant Solutions of Two Kinds of Population Balance Equations with Fragmentation Processes

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,贵阳550025

出　　处：《应用数学学报》2024年第2期255-268,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11761018);贵州省科技计划基金(黔科合基础-ZK[2022]一般021);贵州省高等学校系统建模与数据挖掘重点实验室(No.2023013);贵州省教育厅自然科学研究项目(黔教技[2023]063号);贵州省科技厅科技计划项目(黔科合支撑[2023]一般372)资助。

摘　　要：针对难找到破碎群体平衡方程的精确解和解析方法缺乏的问题,研究两类积分-偏微分方程(破碎群体平衡方程)接受的李群、群不变解、约化积分-常微分方程及精确解.首先采用伸缩变换李群分析方法探寻积分-偏微分方程接受的李群.其次将积分-偏微分方程转化为纯偏微分方程,运用经典李群分析方法计算纯偏微分方程接受的李群.然后利用改进了的李群分析方法结合伸缩变换群和经典李群分析方法获得的结果确定积分-偏微分方程接受的李群.最后找到了积分-偏微分方程接受的李群,给出了积分-偏微分方程的约化积分-常微分方程、群不变解及显式精确解,分析了部分解的动力学行为性质及特征.In this work,aiming at the problem of lacking analytical methods and it is typically difficult to find explicit exact solutions to the population balance equations with fragmentation processes.We consider the admitted Lie groups,group invariant solutions,reduced integro-ordinary differential equations and explicit exact solutions of two classes of integro-partial differential equations(population balance equations with fragmentation processes)by use of the method of scaling transformation group analy-sis,the method of classical Lie group analysis and the method of developed Lie group analysis.Firstly,the admitted scaling transformation Lie groups of the integro-partial differential equations are explored by using the method of scaling transformation group analysis.Secondly,the integro-partial differential equations are transformed into pure partial differential equations,the admitted Lie groups of the pure partial differential equations are calculated by use of the methods of classical Lie group analysis.Thirdly,the admitted Lie groups of the original integro-partial differential equations are deter-mined by use of the methods of developed Lie group analysis combining with the related results obtained by method of scaling transformation group and the method of classi-cal Lie group analysis.Finally,the admitted Lie groups of the original integro-partial differential equations are successfully found.All group invariant solutions,reduced integro-ordinary differential equations and explicit exact solutions are given.The re-lated analysis for dynamic behavior characteristics of a solution with evolution of the size distribution are also presented.

关 键 词：群体平衡方程 破粹过程 李群 群不变解 

分 类 号：O175.5[理学—数学] O175.6[理学—基础数学]