Abstract：An application of the Lie group analysis method as developed for integrodifferential equations (population balance equation) is quite complicated, due to the fact that solving the determining equations of integro-differential equations is typically difficult. Even more, the ways of solving determining equations depend on the original integrodifferential equations studied. Conversely, for simplicity and convenience, the study of new integro-differential equations is started by considering the self-similar solutions using a scaling group. Population balance equations considered in the present paper involve both a partial differential equation and integro-differential equation. All explicit physical solutions and self-similar solutions were presented by using the scaling group analysis method. Analysis of the reduced equations was also provided.
林府标, 张千宏. 用伸缩变换群分析法探究群体平衡方程的自相似解[J]. 应用数学学报, 2020, 43(5): 833-852.
LIN Fubiao, ZHANG Qianhong. Self-similar Solutions of the Population Balance Equation, Using Scaling Group Analysis. Acta Mathematicae Applicatae Sinica, 2020, 43(5): 833-852.
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2020, Vol. 43 
