Asymptotic behavior of Riemann solutions to a hyperbolic system arising from a traffic flow model

Abstract

This paper is mainly concerned with the Riemann problem for a hyperbolic system arising from a traffic flow model, whose Riemann solutions are obtained constructively in terms of the fine analysis of elementary waves. Especially, the Dirac delta shock wave is involved in the Riemann solution at some specially designated initial data. Then, the limiting behavior of Riemann solutions is investigated carefully from the current system to the pressureless Euler system by sending the perturbed parameter tend to zero, in which more complicated nonlinear phenomena of cavitation and concentration than before can be observed and analyzed during this limiting process. Finally, several representative numerical examples are offered to confirm our theoretical results.