Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (1): 237-258.

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

Weifeng Jiang1, Tingting Chen2, Tong Li3, Zhen Wang4,†

1. 1. College of Science, Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province, China Jiliang University, Hangzhou 310018, China;
2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China;
3. Department of Mathematics, The University of Iowa, IA 52246, USA;
4. Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China
• Received:2021-06-16 Revised:2022-06-12 Published:2023-03-01
• Contact: †Zhen WANG.E-mail: zwang@whut.edu.cn
• About author:Weifeng Jiang, E-mail:casujiang89@gmail.com; Tingting Chen, E-mail: chenting0617@163.com;Tong Li, E-mail: tong-li@uiowa.edu
• Supported by:
*Natural Science Foundation of Zhejiang (LQ18A010004), Matematical Analysis, The First class courses in Zhejiang Province (210052), the Fundamental Research Funds for the Provincial Universities of Zhejiang (210039). The research of Zhen Wang was supported by the National Natural Science Foundation of China (11771442).

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.

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