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

doi:10.1007/s10473-023-0114-7

Abstract

Abstract: 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 piecewise constants. Moreover, we analyze different kinds of wave interactions, including the interactions of the $\delta$-shock waves with elementary waves.

Key words: Riemann problem, non-isentropic improved Aw-Rascle-Zhang model, $\delta$-shock wave, wave interactions, traffic flow

Weifeng Jiang, Tingting Chen, Tong Li, Zhen Wang. THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE NON-ISENTROPIC IMPROVED AW-RASCLE-ZHANG MODEL^*[J].Acta mathematica scientia,Series B, 2023, 43(1): 237-258.

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References

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

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