一类细胞分裂群体平衡方程的对称群及精确解

Symmetry Groups and Exact Solutions of a Class of Population Balance Equations with Cells Fission Processes

研究一类细胞分裂群体平衡方程(积分-偏微分方程)的对称群、约化积分-常微分方程、群不变解、显式精确解及解的动力学行为.首先,把积分-偏微分方程转化成纯偏微分方程,然后利用经典李群分析方法计算纯偏微分方程的对称群.其次,采用改进了的李群分析方法结合经典李群分析方法获得的结果确认积分-偏微分方程的对称群.最后,找到积分-偏微分方程的对称群、约化积分-常微分方程、群不变解、显式精确解.运用矩方法获得细胞质量分布的零阶矩和一阶矩,分析了精确解的动力学行为及特征.

Symmetry groups,reduced integro-ordinary differential equations,group invariant solutions,explicit exact solutions and dynamic behavior of solutions of a class of population balance equations(integro-partial differential equations)with cells fission processes are considered here.Firstly,an integro-partial differential equation is transformed into a pure partial differential equation,whose symmetry groups are determined by use of the methods of classical Lie group analysis.Secondly,symmetry groups of the original integro-partial differential equation are determined by use of the methods of developed Lie group analysis combining with the related results obtained by methods of classical Lie group analysis.Finally,symmetry groups of the original integro-partial differential equation are found.All group invariant solutions,reduced integro-ordinary differential equations and explicit exact solutions are given.The zero-th moment and first moment of cells mass distribution are provided by using the methods of moments.The related analysis for dynamic behavior characteristics of a solution with evolution of the cells fission distribution are also presented.