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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (4): 55-65.doi: 10.6040/j.issn.1671-9352.0.2021.228

• • 上一篇    

相对论Chaplygin气体欧拉方程组的阴影波解

贾艺菲,郭俐辉*,白寅松   

  1. 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046
  • 发布日期:2022-03-29
  • 作者简介:贾艺菲(1996— ),女,硕士研究生,研究方向为偏微分方程及其应用. E-mail:jiayifei333@163.com*通信作者简介:郭俐辉(1979— ),男,博士,教授,研究方向为偏微分方程及其应用. E-mail:lihguo@126.com
  • 基金资助:
    国家自然科学基金资助项目(11761068);新疆维吾尔自治区自然科学基金资助项目(2019Q015,2017D01C053)

Shadow wave solution for the relativistic Chaplygin Euler equations

JIA Yi-fei, GUO Li-hui*, BAI Yin-song   

  1. School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Published:2022-03-29

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摘要： 研究了相对论Chaplygin气体欧拉方程组的阴影波解的存在性,利用超压缩熵条件确定了阴影波解的弱唯一性,最后在Schwartz广义函数意义下,证明了超压缩阴影波解收敛到delta激波解。

关键词: 相对论欧拉方程组, Chaplygin气体, 阴影波, delta激波

Abstract: The main purpose of this article is to construct the shadow wave solution of the relativistic Chaplygin Euler equations. To ensure the weak uniqueness of the shadow wave solution, the over-compressive entropy condition is used as the admissibility criteria. Finally, in the sense of Schwartz generalized function, it is proved that the over-compressive shadow wave solution converges to the delta shock wave solution.

Key words: relativistic Euler equations, Chaplygin gas, shadow wave, delta shock wave

中图分类号: 

  • O175.27
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