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Riemann Problem and Wave Interactions for a Class of Strictly Hyperbolic Systems of Conservation Laws

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Abstract

A class of strictly hyperbolic systems of conservation laws are proposed and studied. Firstly, the Riemann problem with initial data of two piecewise constant states is constructively solved. The solutions involving contact discontinuities and delta shock waves are obtained. The generalized Rankine–Hugoniot relation and entropy condition for the delta shock wave are clarified and the existence and uniqueness of the delta-shock solution is proved. Furthermore, the global structure of solutions with five different configurations is constructed via investigating the interactions of delta shock waves and contact discontinuities. Finally, we present a typical example to illustrate the application of the system introduced.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan Normal University, Kunming, 650500, People’s Republic of China

    Yu Zhang

  2. College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China

    Yanyan Zhang

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  1. Yu Zhang
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  2. Yanyan Zhang
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Correspondence to Yu Zhang.

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Supported by National Science Foundation of China (11501488), Yunnan Applied Basic Research Projects (2018FD015), the Scientific Research Foundation Project of Yunnan Education Department (2018JS150) and Nan Hu Young Scholar Supporting Program of XYNU.

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Zhang, Y., Zhang, Y. Riemann Problem and Wave Interactions for a Class of Strictly Hyperbolic Systems of Conservation Laws. Bull Braz Math Soc, New Series 51, 1017–1040 (2020). https://doi.org/10.1007/s00574-019-00186-5

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  • DOI: https://doi.org/10.1007/s00574-019-00186-5

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