一类2+1维群体平衡方程的尺度变换群分析及自相似解

Analysis of scaling transformation group and self-similar solutions to a class of 2+1 dimensional population balance equation

该文研究一类2+1维既有聚合又有破损过程的群体平衡方程.用尺度变换群方法获得了方程接受的尺度变换群、自相似解、精确解和约化方程.研究结果表明尺度变换群方法不但可用于群体平衡方程,而且不需要很困难地求解决定方程.

In this paper,a class of 2+1 dimensional population balance equation with both aggregation and breakage processes occur together was investigated.The admitted scaling group,self-similar solutions,exact solutions and corresponding reduced equations of this population balance equation were presented by use of the method of scaling transformation group.The obtained results show that the method of scaling transformation group can be used not only for population balance equations,but also no need to solve the determining equation very difficultly.