一类带齐次凝聚核的Smoluchowski方程的尺度变换群及相似解

Scaling transformation group and similarity solutions for a class of Smoluchowski equation with homogeneous coagulation kernels

研究一类带齐次凝聚核的积分-偏微分Smoluchowski方程的相似解及解法.首先用量纲分析法减少方程中必不可少的独立常量的数量;其次,用尺度变换群研究方程的相似不变量及相似解的可行性,构造自相似解和约化的积分-常微分方程;最后,用解的群变换和自相似解构造相似解.

Similarity solutions and analytical solving methods of a class of integro-partial differential Smoluchowski equation with homogeneous coagulation kernels are investigated in this work.Firstly,the numbers of essential independent quantities of the original equations were reduced by use of the dimensional analysis.Secondly,the feasibility of the similarity invariant variables and similarity solutions of the original equations were studied by the method of scaling transformation group analysis,self-similar solutions and reduced integro-ordinary differential equations are constructed by using similarity invariant variables of scaling functions.Finally,similarity solutions of the original equations are constructed by use of the self-similar solutions and group transformation of solutions.