Smoluchowski方程的对称与显式解析解  

Symmetries and Explicit Analytical Solutions of the Smoluchowski Coagulation Equation

作　　者：林府标 张千宏 LIN Fubiao;ZHANG Qianhong(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang,Guizhou,550025,P.R.China)

机构地区：[1]贵州财经大学数统学院,贵阳贵州550025

出　　处：《数学进展》2018年第6期833-843,共11页Advances in Mathematics（China）

基　　金：2018年度贵州财经大学校级科研基金项目资助(No.2018XYB04)

摘　　要：研究了一类带齐次核函数的偏微分一积分Smoluchowski方程.利用发展了的李群分析方法给出了带齐次核函数的Smoluchowski方程的决定方程的通解、对称、最优子李代数系统、约化的常微分—积分方程、群不变解和显式解析解.A class of integro-differential Smoluchowski coagulation equation with homoge- neous coagulation kernel is considered. We present the developed Lie group analysis method for the Smoluchowski coagulation equation with homogeneous coagulation kernel. The determining equations are solved, the optimal system, symmetries, invariant solutions and all the reduced equations are obtained. Furthermore, an explicit analytical physical solution is also provided.

关 键 词：微分一积分方程 SMOLUCHOWSKI方程 李群分析法 群不变解 显式解析解 

分 类 号：O175.5[理学—数学] O175.6[理学—基础数学]