| 一类带齐次分裂核的群体平衡方程的相似分析及相似解 |
| |
| 引用本文： | 林府标,王 骞,张千宏.一类带齐次分裂核的群体平衡方程的相似分析及相似解[J].江西师范大学学报(自然科学版),2022,0(2):215-220. |
| |
| 作者姓名： | 林府标 王 骞 张千宏 |
| |
| 作者单位： | 1.贵州财经大学数统学院,贵州 贵阳 550025; 2.贵州师范大学附属中学,贵州 贵阳 550001 |
| |
| 摘 要： | 该文研究一类带齐次分裂核的群体平衡方程的相似分析及相似解.首先将尺度变换群法用于一类带齐次分裂核的群体平衡方程, 探寻尺度函数的相似不变量,用自相似不变量构造自相似解; 其次用解的群变换和自相似解获得了原方程的相似解、显式精确解、约化方程, 分析了解的动力学性态; 最后,相似分析结果表明:尺度变换群法不仅可用于纯微分方程, 而且可用于群体平衡方程.
|
| 关 键 词： | 群体平衡方程 尺度变换群 相似不变量 相似解 |
The Similarity Analysis and Solutions of a Class of Population Balance Equations with Homogeneous Fragmentation Kernels |
| |
| LIN Fubiao,WANG Qian,ZHANG Qianhong.The Similarity Analysis and Solutions of a Class of Population Balance Equations with Homogeneous Fragmentation Kernels[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2022,0(2):215-220. |
| |
| Authors: | LIN Fubiao WANG Qian ZHANG Qianhong |
| |
| Affiliation: | 1.School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang Guizhou 550025,China; 2.The Middle School Attached to the Guizhou Normal University,Guiyang Guizhou 550001,China |
| |
| Abstract: | The similarity analysis and solutions of a class of population balance equations with homogeneous fragmentation kernels are studied in this paper.Firstly,the method of scaling transformation group is applied to a class of population balance equations with homogeneous fragmentation kernels to explore the similarity invariant variables of scaling functions.The self-similar solutions are constructed by the self-similar invariant variables.Secondly,the similarity solutions,exact explicit solutions and reduced integro-ordinary differential equations of the original equations are obtained by using group transformation of solutions and self-similar solutions.The analysis of dynamic behavior of solution is also presented.Finally,the similarity analysis results show that the scaling transformation group can not only be used for pure differential equations,but also be applied to population balance equations. |
| |
| Keywords: | population balance equation scaling transformation group similarity invariant variable similarity solution |
|
| 点击此处可从《江西师范大学学报(自然科学版)》浏览原始摘要信息 |
|
点击此处可从《江西师范大学学报(自然科学版)》下载全文 |
