Two-dimensional Aw–Rascle model with Chaplygin pressures: Riemann solutions consisting of contact discontinuities

Abstract

The two-dimensional Aw–Rascle model can describe the traffic flow with lane changing. We are interested in the four-wave Riemann problem for the two-dimensional Aw–Rascle model with Chaplygin pressures, which is fully linearly degenerate. The contact discontinuity and $\delta$-shock wave may develop in solutions. We are concerned with the solutions only involving contact discontinuities. As a result, twelve kinds of structures are derived.