探求一类群体平衡方程的显式精确解. 首先将群体平衡方程转化成偏微分方程, 利用经典李群分析法获得了偏微分方程的对称, 进而得到了群体平衡方程的对称、最优化子李代数系统、约化的常微分-积分方程、群不变解及精确解. 其次采用试探函数法找到了约化的常微分-积分方程的部分精确解, 最后得到了群体平衡方程的部分显式精确解.
In this paper, exact solutions for a class of population balance equations were investigated. The population balance equation was first transformed to a partial differential equation; symmetries of the partial differential equation were then obtained by use of the classical Lie group analysis method. In addition, the paper presents symmetries, optimal system of subalgebras, reduced ordinary differential integral equations, and group invariant solutions of the population balance equation. Exact solutions of the reduced ordinary differential integral equations were subsequently found using trial functions. Finally, exact solutions for a class of population balance equations are derived.
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