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

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.