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Global solutions of shock reflection problem for the pressure gradient system

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The first author is supported by NSF of Yunnan University (No. 2019FY003007). The third author is supported by National Natural Science Foundation of China (No. 11761077) and Key Project of Yunnan Provincial Science and Technology Department and Yunnan University (No. 2018FY001(-014))

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  • We are concerned with the shock reflection in gas dynamics for the pressure gradient system. Experimental and computational analysis has shown that two patterns of regular reflection may occur: supersonic and subsonic reflection. In this paper we establish the global existence of solutions for both configurations. The ideas and techniques developed here will be useful for the two-dimensional Riemann problems for hyperbolic conservation laws.

    Mathematics Subject Classification: Primary: 35L50, 35L67, 76H05; Secondary: 35J67.


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  • Figure 1.  Supersonic regular shock reflection configuration(left); subsonic regular shock reflection configuration (right)}

    Figure 2.  Hypothetical curves

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