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Subsonic solutions to a shock diffraction problem by a convex cornered wedge for the pressure gradient system

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The research of Qin Wang is supported by NNSF of China (No. 11761077), Project of Yunnan University (No. 2019FY003007) and Program for Innovative Research Team (in Science and Technology) in Universities of Yunnan Province. The research of Kyungwoo Song is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1F1A1057766)

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  • We establish the global existence of subsonic solutions to a two dimensional Riemann problem governed by a self-similar pressure gradient system for shock diffraction by a convex cornered wedge. Since the boundary of the subsonic region consists of a transonic shock and a part of a sonic circle, the governing equation becomes a free boundary problem for nonlinear degenerate elliptic equation of second order with a degenerate oblique derivative boundary condition. We also obtain the optimal $ C^{0,1} $-regularity of the solutions across the degenerate sonic boundary.

    Mathematics Subject Classification: Primary: 35L50, 35L67, 35J70.


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  • Figure 1.  Shock $ S_0 $ passes the wedge at $ t = 0 $

    Figure 2.  Shock diffraction configuration

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