一类积分-偏微分群体平衡方程的非完全不变群及显式精确解

Incomplete Invariant Groups and Explicit Exact Solutions of A Class of Integro-partial Differential Population Balance Equation

文章研究一类积分-偏微分群体平衡方程的非完全不变群、群不变解和显式精确解及解的动力学行为和特征:首先,利用尺度变换群法探索群体平衡方程的不变群;其次,将积分-偏微分方程转化成纯偏微分方程,采用经典李群分析方法探究纯偏微分方程的完全不变群,应用改进的李群分析方法验证原群体平衡方程的非完全不变群;最后,给出了原群体平衡方程的非完全不变群、群不变解、约化积分-常微分方程及显式精确解,研究了部分解蕴藏的动力学性态及特征。

Incomplete invariant groups,group invariant solutions,explicit exact solutions and dynamic behavior characteristics of solutions of a class of integro-partial differential population balance equation were investigated in this work.Firstly,admitted scaling transformation Lie groups of the population balance equation were explored by using the methods of scaling transformation group analysis.Secondly,an integro-partial differential population ba-lance equation was transformed into a pure partial differential equation,complete admitted Lie groups of the pure partial differential equation were studied by using the method of classical Lie group analysis.Thirdly,incomplete admitted Lie groups of the original integro-partial differential population balance equation were verified by using the methods of developed Lie group analysis.Finally,incomplete invariant groups of the original integro-partial diffe-rential population balance equation were found.All group invariant solutions,reduced integro-ordinary differential equations and explicit exact solutions were also given.The related analysis for dynamic behavior characteristics of solutions with evolution of the size distribution were also presented.