一类群体平衡方程的李群分析及精确解

doi:10.3969/j.issn.1000-5641.201911008

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (2): 15-22.doi: 10.3969/j.issn.1000-5641.201911008

一类群体平衡方程的李群分析及精确解

林府标, 张千宏

贵州财经大学数统学院, 贵阳　550025

收稿日期:2019-02-03 发布日期:2020-03-16
作者简介:林府标,男,博士,讲师,研究方向为李群分析法在微分方程中的应用.E-mail:linfubiao0851@163.com
基金资助:
国家自然科学基金（11761018，11361012）；贵州省科技计划基金项目（黔科合基础[2019]1051）；贵州省教育厅青年科技人才成长项目（黔教合KY字[2017]150）；2018年度贵州财经大学校级科研基金项目（2018XYB04）

Lie group analysis and exact solutions for a class of population balance equations

LIN Fubiao, ZHANG Qianhong

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang　550025, China

Received:2019-02-03 Published:2020-03-16

摘要/Abstract

摘要： 探求一类群体平衡方程的显式精确解. 首先将群体平衡方程转化成偏微分方程, 利用经典李群分析法获得了偏微分方程的对称, 进而得到了群体平衡方程的对称、最优化子李代数系统、约化的常微分-积分方程、群不变解及精确解. 其次采用试探函数法找到了约化的常微分-积分方程的部分精确解, 最后得到了群体平衡方程的部分显式精确解.

关键词: 群体平衡方程, 李群分析法, 试探函数法, 群不变解, 精确解

Abstract: In this paper, exact solutions for a class of population balance equations were investigated. The population balance equation was first transformed to a partial differential equation; symmetries of the partial differential equation were then obtained by use of the classical Lie group analysis method. In addition, the paper presents symmetries, optimal system of subalgebras, reduced ordinary differential integral equations, and group invariant solutions of the population balance equation. Exact solutions of the reduced ordinary differential integral equations were subsequently found using trial functions. Finally, exact solutions for a class of population balance equations are derived.

Key words: population balance equation, Lie group analysis method, method of trial function, group invariant solution, exact solution

中图分类号:

林府标, 张千宏. 一类群体平衡方程的李群分析及精确解[J]. 华东师范大学学报（自然科学版）, 2020, 2020(2): 15-22.

LIN Fubiao, ZHANG Qianhong. Lie group analysis and exact solutions for a class of population balance equations[J]. Journal of East China Normal University(Natural Science), 2020, 2020(2): 15-22.

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一类群体平衡方程的李群分析及精确解

Lie group analysis and exact solutions for a class of population balance equations

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