[1]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,(02):215-220.[doi:10.16357/j.cnki.issn1000-5862.2022.02.15]
　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 Science Edition,2022,(02):215-220.[doi:10.16357/j.cnki.issn1000-5862.2022.02.15]
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一类带齐次分裂核的群体平衡方程的相似分析及相似解()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年02期
页码:
215-220
栏目:
数学与应用数学
出版日期:
2022-03-25

文章信息/Info

Title:
The Similarity Analysis and Solutions of a Class of Population Balance Equations with Homogeneous Fragmentation Kernels
文章编号:
1000-5862(2022)02-0215-06
作者:
林府标1; 王 骞2; 张千宏1
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
Author(s):
LIN Fubiao1; WANG Qian2; ZHANG Qianhong1
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
关键词:
群体平衡方程;  尺度变换群;  相似不变量;  相似解
Keywords:
population balance equation;  scaling transformation group;  similarity invariant variable;  similarity solution
分类号:
O 175.5; O 175.6
DOI:
10.16357/j.cnki.issn1000-5862.2022.02.15
文献标志码:
A
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.
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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2021-07-20
基金项目:国家自然科学基金(11761018,11361012),贵州省科技计划基金(黔科合基础-ZK[2022]一般021),贵州省科技厅科学技术基金([2020]1Y008)和贵州省教育厅创新群体(黔教合KY字[2021]015)资助项目.
作者简介:林府标(1978—),男,贵州盘州人,副教授,博士,主要从事偏微分方程研究.E-mail:linfubiao0851@163.com
更新日期/Last Update: 2022-03-25