@article{He2026, 
author = {Weihua He and Lihui Guo},
title = {The Asymptotic Limit of the Riemann Solution for the Macroscopic Production Model with Anti-Chaplygin Gas},
year = {2026},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {43},
number = {2},
pages = {183-195},
keywords = {macroscopic production model, anti-Chaplygin gas, Riemann problem, numerical simulation},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2025.03.02.0001},
doi = {10.13568/j.cnki.651094.651316.2025.03.02.0001},
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 (J1 + R2), a combination of contact discontinuity and shock wave (J1 + S2), and Dirac shock wave (δS). Secondly, the pressure vanishing limit of the macroscopic production model of the anti-Chaplygin gas is studied. As the perturbation parameter ε decreases to the parameter ε0, which is dependent only on the initial data, it is proved that the Riemann solution (J1 + S2) converges to the δS of the anti-Chaplygin gas state equation. Moreover, when ε eventually approaches 0, the δS converges to the δS of the transport equation. Additionally, it is proved that the Riemann solution (J1 + R2) converges to the vacuum solution of the transport equation. Finally, we present some representative numerical experimental results.}
}