# American Institute of Mathematical Sciences

October  2020, 19(10): 4899-4920. doi: 10.3934/cpaa.2020217

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

 1 Department of Mathematics, Yunnan University, Kunming 650091, China 2 Department of Mathematics, Kyung Hee University, Seoul 02447, Korea

* Corresponding author

Received  December 2019 Revised  June 2020 Published  July 2020

Fund Project: 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)

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.

Citation: Yinzheng Sun, Qin Wang, Kyungwoo Song. Subsonic solutions to a shock diffraction problem by a convex cornered wedge for the pressure gradient system. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4899-4920. doi: 10.3934/cpaa.2020217
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##### References:
Shock $S_0$ passes the wedge at $t = 0$
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