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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (10): 89-100.doi: 10.6040/j.issn.1671-9352.0.2023.165

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三元简化色谱方程组的阴影波解

杨帆(),郭俐辉*()   

  1. 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046
  • 收稿日期:2023-04-18 出版日期:2024-10-20 发布日期:2024-10-10
  • 通讯作者: 郭俐辉 E-mail:yf199906@163.com;lihguo@126.com
  • 作者简介:杨帆(1999—)，男，硕士研究生，研究方向为偏微分方程及其应用. E-mail: yf199906@163.com
  • 基金资助:
    国家自然科学基金资助项目(12161084);国家自然科学基金资助项目(11961063);；新疆维吾尔族自治区自然科学基金资助项目(2022D01E42);新疆应用数学自治区重点实验室资助项目(XJDX1401)

Shadow wave solutions for ternary simplified chromatography equations

Fan YANG(),Lihui GUO*()   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Received:2023-04-18 Online:2024-10-20 Published:2024-10-10
  • Contact: Lihui GUO E-mail:yf199906@163.com;lihguo@126.com

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摘要：

主要研究三元简化色谱方程组黎曼解的整体结构及阴影波解的存在性和收敛性。根据黎曼初值，将黎曼问题分6种情形进行讨论，得到三元简化色谱方程组的黎曼解。当-1＜p-≤0≤p+时，证明阴影波解在Schwartz广义函数意义下的存在性和收敛性。最后，给出数值模拟。

关键词: 色谱方程组, 阴影波, 狄拉克激波, 黎曼问题

Abstract:

This paper mainly considers the overall structure of Riemann solution and the existence and convergence of shadow wave solutions of the ternary simplified chromatography equations. According to Riemann initial data, and Riemann problem is divided into six different cases, Riemann solutions for the ternary simplified chromatography equations are obtained. When -1 < p-≤0≤p+, the existence and convergence of shadow wave solutions in the sense of Schwartz distributions are proved. Finally, numerical simulation is given.

Key words: chromatography equation, shadow wave, delta shock, Riemann problem

中图分类号: 

  • O175.27

图1

当0＜p-＜p+时黎曼问题(1)、(2)的解S+J"

图2

当0≤ p+＜p-时黎曼问题(1)、(2)的解R+J"

图3

当-1＜p+＜0＜p-时黎曼问题(1)、(2)的解R1+(0, 0)+R2"

图4

当-1＜p-＜p+＜0时黎曼问题(1)、(2)的解J+S"

图5

当-1＜p+＜p-≤0时黎曼问题(1)、(2)的解J+R"

图6

黎曼问题(1)、(2)的阴影波解和狄拉克激波解"

图7

情形-1＜p-≤0≤p+时的数值结果"

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[1] 贾艺菲,郭俐辉,白寅松. 相对论Chaplygin气体欧拉方程组的阴影波解[J]. 《山东大学学报(理学版)》, 2022, 57(4): 55-65.
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