SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1579-1629, January 2021.
We are concerned with the sonic-supersonic structures extracted from the transonic flow problems in gas dynamics. A local classical supersonic solution for the two-dimensional steady full Euler equations is established in an angular region bounded by the sonic curve and the characteristic curve. In order to overcome the challenges caused by the coupling of nonlinearity and degeneracy at the corner point, we develop a new iteration pattern to show the convergence of the iterative sequence generated by the Euler equations in terms of a partial hodograph coordinate system. The pattern developed here will be useful for studying the degenerate mixed-type boundary value problems for other related nonlinear hyperbolic systems.

中文翻译：

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二维全欧拉方程混合型边值问题的音速-超音速解

SIAM数学分析杂志，第53卷，第2期，第1579-1629页，2021年1月。
我们关注从气体动力学中跨音速流动问题中提取的音速-超音速结构。在以声波曲线和特征曲线为边界的角区域中，建立了二维稳态全欧拉方程的局部经典超音速解决方案。为了克服在拐角处非线性和简并性耦合所带来的挑战，我们开发了一种新的迭代模式，以用部分Hodograph坐标系表示由Euler方程生成的迭代序列的收敛性。此处开发的模式对于研究其他相关的非线性双曲系统的退化混合型边值问题将很有用。