The Asymptotic Limit of the Riemann Solution for the Macroscopic Production Model with Anti-Chaplygin Gas

He Weihua; Guo Lihui

doi:10.13568/j.cnki.651094.651316.2025.03.02.0001

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The Asymptotic Limit of the Riemann Solution for the Macroscopic Production Model with Anti-Chaplygin Gas

Intelligent Modeling and Engineering Computation | 更新时间：2026-03-24

- The Asymptotic Limit of the Riemann Solution for the Macroscopic Production Model with Anti-Chaplygin Gas
- Journal of Xinjiang University(Natural Science Edition in Chinese and English) Vol. 43, Issue 2, Pages: 183-195(2026)
- 作者机构：
  
  新疆大学数学与系统科学学院，新疆乌鲁木齐 830017
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2025.03.02.0001
  CLC： O175.24
- Received：02 March 2025，
  
  Revised：2026-02-05，
  
  Accepted：06 February 2026，
  
  Published：25 March 2026
- 稿件说明：
移动端阅览
何伟华，郭俐辉．预期因子为反Chaplygin气体宏观生产模型黎曼解的渐近极限［J］．新疆大学学报（自然科学版中英文），2026，43（2）：183-195．

He Weihua，Guo Lihui．The asymptotic limit of the Riemann solution for the macroscopic production model with anti-Chaplygin gas［J］．Journal of Xinjiang University（Natural Science Edition in Chinese and English），2026，43（2）：183-195.
何伟华，郭俐辉．预期因子为反Chaplygin气体宏观生产模型黎曼解的渐近极限［J］．新疆大学学报（自然科学版中英文），2026，43（2）：183-195． DOI： 10.13568/j.cnki.651094.651316.2025.03.02.0001.

He Weihua，Guo Lihui．The asymptotic limit of the Riemann solution for the macroscopic production model with anti-Chaplygin gas［J］．Journal of Xinjiang University（Natural Science Edition in Chinese and English），2026，43（2）：183-195. DOI： 10.13568/j.cnki.651094.651316.2025.03.02.0001.

摘要

本文主要研究预期因子为反Chaplygin气体宏观生产模型黎曼解的极限行为．首先，研究模型的黎曼问题，得到3种黎曼解的结构：接触间断和疏散波组合（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578568&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578579&type=

9.31333351

3.30200005

），接触间断和激波组合（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578569&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578580&type=

8.97466660

3.30200005

），狄拉克激波（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578570&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578581&type=

3.21733332

2.28600001

）．其次，研究反Chaplygin气体宏观生产模型的压力消失极限．当扰动参数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578560&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578593&type=

1.26999998

2.28600001

减小到仅依赖初值的参数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578561&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578594&type=

2.28600001

3.21733332

时，证明黎曼解（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578562&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578595&type=

8.97466660

3.30200005

）收敛到反Chaplygin气体状态方程的

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578570&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578581&type=

3.21733332

2.28600001

．且当

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578560&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578593&type=

1.26999998

2.28600001

最终趋于0时，证明

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578608&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578596&type=

3.21733332

2.28600001

收敛到输运方程的

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578586&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578597&type=

3.21733332

2.28600001

；此外，还证明黎曼解（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578587&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578575&type=

9.31333351

3.30200005

）收敛到输运方程的真空解．最后，给出具有代表性的实验结果数值．

Abstract

This paper mainly studies the limit behavior of Riemann solutions for the macroscopic production model with anti-Chaplygin gas. Firstly

we investigate the Riemann problem associated with this model. Three types of Riemann solutions are obtained: a combination of contact discontinuity and rarefaction wave

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578588&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578576&type=

12.19200039

3.89466691

a combination of contact discontinuity and shock wave

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578589&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578577&type=

12.53066730

3.89466691

and Dirac shock wave

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578601&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578623&type=

6.09600019

2.87866688

. Secondly

the pressure vanishing limit of the macroscopic production model of the anti-Chaplygin gas is studied. As the perturbation parameter

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578613&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578590&type=

2.62466669

2.37066650

decreases to the parameter

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578591&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578602&type=

3.38666677

3.30200005

which is dependent only on the initial data

it is proved that the Riemann solution (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578625&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578614&type=

9.31333351

3.30200005

) converges to the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578592&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578603&type=

4.40266657

2.37066650

of the anti-Chaplygin gas state equation. Moreover

when

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578616&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578615&type=

2.62466669

2.37066650

eventually approaches 0

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578604&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578626&type=

0.67733335

0.84666669

the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578592&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578603&type=

4.40266657

2.37066650

converges to the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578592&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578603&type=

4.40266657

2.37066650

of the transport equation. Additionally

it is proved that the Riemann solution (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578627&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102578638&type=

9.31333351

3.30200005

) converges to the vacuum solution of the transport equation. Finally

we present some representative numerical experimental results.

关键词

Keywords

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