数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 57-82.doi: 10.1007/s10473-019-0106-9

• 论文 • 上一篇    下一篇

GLOBAL SOLUTIONS OF THE PERTURBED RIEMANN PROBLEM FOR THE CHROMATOGRAPHY EQUATIONS

张婷, 盛万成   

  1. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, China
  • 收稿日期:2017-11-30 修回日期:2018-05-18 出版日期:2019-02-25 发布日期:2019-03-13
  • 通讯作者: Wancheng SHENG E-mail:mathwcsheng@shu.edu.cn
  • 作者简介:Ting ZHANG,zhangting123@i.shu.edu.cn
  • 基金资助:
    Supported by NSFC (11371240 and 11771274), and the grant of "The First-Class Discipline of Universities in Shanghai".

GLOBAL SOLUTIONS OF THE PERTURBED RIEMANN PROBLEM FOR THE CHROMATOGRAPHY EQUATIONS

Ting ZHANG, Wancheng SHENG   

  1. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, China
  • Received:2017-11-30 Revised:2018-05-18 Online:2019-02-25 Published:2019-03-13
  • Contact: Wancheng SHENG E-mail:mathwcsheng@shu.edu.cn
  • Supported by:
    Supported by NSFC (11371240 and 11771274), and the grant of "The First-Class Discipline of Universities in Shanghai".

摘要: The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.

关键词: Riemann problem, chromatography equation, wave interactions, Temple class, hyperbolic conservation laws

Abstract: The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.

Key words: Riemann problem, chromatography equation, wave interactions, Temple class, hyperbolic conservation laws