THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE NON-ISENTROPIC IMPROVED AW-RASCLE-ZHANG MODEL

In this paper, we study the Radon measure initial value problem for the non-isentropic improved Aw-Rascle-Zhang model. For arbitrary convex F(u) in this model we construct the Riemann solutions by elementary waves and delta-shock waves using the method of generalized characteristic analysis. We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piece-wise constants. Moreover, we analyze different kinds of wave interactions, including the interactions of the delta-shock waves with elementary waves.

Automated summary

In this paper, we investigate the Radon measure initial value problem for the non-isentropic improved Aw-Rascle-Zhang model. We construct the Riemann solutions, including elementary waves and delta-shock waves, for arbitrary convex F(u) in this model using the method of generalized characteristic analysis. By considering the limit of solutions for initial data with three piece-wise constants, we obtain the constructive solutions for initial data containing the Dirac measure. Additionally, we analyze various wave interactions, including the interactions of delta-shock waves with elementary waves.