带有Riemann初值简化色谱方程组的初边值问题

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (6): 1333-1344.

带有Riemann初值简化色谱方程组的初边值问题

刘冬冬¹, 俞康宁², 郭俐辉¹

1. 新疆大学数学与系统科学学院, 乌鲁木齐 830046; 2. 昌吉学院数学系, 新疆昌吉 831100

收稿日期:2021-03-19 出版日期:2021-11-26 发布日期:2021-11-26
通讯作者: 郭俐辉 E-mail:lihguo@126.com

Initial Boundary Value Problem of Simplified Chromatography Equations with Riemannian Initial Value

LIU Dongdong¹, YU Kangning², GUO Lihui¹

1. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China;
2. Department of Mathematics, Changji University, Changji 831100, Xinjiang Uygur Autonomous Region, China

Received:2021-03-19 Online:2021-11-26 Published:2021-11-26

摘要/Abstract

摘要： 用熵流对和黏性消失法讨论简化色谱方程组的边界熵不等式问题. 首先, 通过判断色谱方程组初值问题的解是否满足边界熵不等式, 给出基本波在边界上相互作用的情况, 进而给出色谱方程组初边值问题的全局解; 其次, 利用数值模拟方法验证初边值问题理论分析的正确性.

关键词: 初边值问题, 熵流对, 波的相互作用, 色谱方程组, Dirac激波

Abstract: The boundary entropy inequality problem of simplified chromatography equation was discussed by using entropy flux pair and
the viscosity vanishing method. Firstly, by judging whether the solutions of the initial value problem of the chromatography equation satisfied the boundary entropy inequality, we gave the interaction of the elementary waves on the boundary, and then gave the global solutions for the initial boundary value problem of the chromatography equation. Secondly, the correctness of the theoretical analysis for the initial boundary value problem was verified by numerical simulation.

Key words: initial boundary value problem, entropy flux pair, wave interaction, chromatography equations, Dirac shock wave

中图分类号:

O175.24

刘冬冬, 俞康宁, 郭俐辉. 带有Riemann初值简化色谱方程组的初边值问题[J]. 吉林大学学报(理学版), 2021, 59(6): 1333-1344.

LIU Dongdong, YU Kangning, GUO Lihui. Initial Boundary Value Problem of Simplified Chromatography Equations with Riemannian Initial Value[J]. Journal of Jilin University Science Edition, 2021, 59(6): 1333-1344.

[1]	袁芳. 一类最优投资的数学问题[J]. 吉林大学学报(理学版), 2016, 54(06): 1193-1198.
[2]	詹华税, 袁洪君. 边界退化的多孔介质方程[J]. 吉林大学学报(理学版), 2015, 53(05): 829-834.
[3]	詹华税, 袁洪君. 边界退化的对流扩散方程[J]. 吉林大学学报(理学版), 2015, 53(03): 353-358.
[4]	任长宇, 袁芳. 一类最优投资理论的数学模型[J]. J4, 2012, 50(05): 829-834.
[5]	任长宇, 陈默, 李志军. 一类一般形式抛物型Monge-Ampère方程的第三初边值问题[J]. J4, 2011, 49(04): 587-593.
[6]	任长宇, 陈默. 一个源于最优投资理论的抛物型Monge-Ampère方程的第一初边值[J]. J4, 2009, 47(05): 866-870.