Delta shocks and vacuums in the Aw–Rascle model with anti van der Waals Chaplygin gas under the flux approximation

Abstract

In this manuscript, we explore the concentration and cavitation phenomena in the Riemann problem for the Aw–Rascle model coupled with an anti van der Waals Chaplygin gas while considering a two-parameter flux approximation. We investigate the presence of a δ-shock and a vacuum state within the Riemann problem for this specific system. Additionally, we incorporate a perturbed flux approximation scheme and analyze the Riemann solution as the values of α1 and α2 approach 0. Our findings demonstrate that the δ-shock solution to the simplified equations can be achieved by examining the Riemann solution that involves two shock waves in the perturbed flux approximation system. This occurs when the flux approximation linked to the anti van der Waals Chaplygin gas model vanishes. Furthermore, the Riemann solution that includes two rarefaction waves converges to the vacuum state solution of the simplified equations.