色谱方程的广义黎曼问题:含有Delta激波

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1300-1313.

色谱方程的广义黎曼问题:含有Delta激波

潘丽君¹,韩欣利^2,*(),李彤³

¹ 南京航空航天大学理学院南京 211106
² 南京邮电大学理学院南京 210023
³ Department of Mathematics, University of Iowa, Iowa city, IA 52242, USA

收稿日期:2017-12-16 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 韩欣利 E-mail:xinlihan@126.com
基金资助:
国家自然科学基金(11301264);中国留学基金、中国博士后基金(2013M531343);中央高校基本科研业务费专项资金(NZ2014107);江苏省优秀中青年教师和校长境外研修项目和江苏省自然科学基金(BK20130779)

The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave

Lijun Pan¹,Xinli Han^2,*(),Tong Li³

¹ College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106
² College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023
³ Department of Mathematics, University of Iowa, Iowa city, IA 52242, USA

Received:2017-12-16 Online:2019-12-26 Published:2019-12-28
Contact: Xinli Han E-mail:xinlihan@126.com
Supported by:
the NSFC(11301264);the China Scholarship Council, the China Postdoctoral Science Foundation(2013M531343);the Fundamental Research Funds for the Central Universities(NZ2014107);the Jiangsu Overseas Research & Training Program for University ProminentYoung & Middle-Aged Teachers and Presidents and the NSF of Jiangsu Province(BK20130779)

摘要/Abstract

摘要：

论文研究了非线性色谱方程的广义黎曼问题，并在x-t平面内，构造性地获得了上述广义黎曼问题的局部解.由于非线性色谱方程的黎曼解含有Delta激波，这与以往其它模型的广义黎曼问题（对应的黎曼解只有古典基本波）有很大区别.论文结果表明：在大多情况，广义黎曼解和对应的黎曼解结构相同；但当相关的黎曼解含有Delta激波时，Delta激波可能会转变成激波和接触间断的组合.论文结果有助于详细分析Delta激波的内部机理.

关键词: 色谱方程, 黎曼问题, 广义黎曼问题, 熵条件, Delta激波

Abstract:

This paper is concerned with the generalized Riemann problem for the nonlinear chromatography equations, where the delta shock wave occurs in the corresponding Riemann solution. It is quite different from the previous generalized Riemann problems which focus on classical elementary waves. We constructively solve the generalized Riemann problem in a neighborhood of the origin on the x-t plane. In solutions, we find that the generalized Riemann solutions have a structure similar to the solution of the corresponding Riemann problem for most of cases. However, a delta shock wave in the corresponding Riemann solution may turn into a shock wave followed by a contact discontinuity, which provides us with a detailed method for analyzing the internal mechanism of a delta shock wave.

Key words: Chromatography equations, Riemann problem, Generalized Riemann problem, Entropy condition, Delta shock wave

中图分类号:

O175.27

潘丽君,韩欣利,李彤. 色谱方程的广义黎曼问题:含有Delta激波[J]. 数学物理学报, 2019, 39(6): 1300-1313.

Lijun Pan,Xinli Han,Tong Li. The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1300-1313.

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