In this paper, we established the global existence of supersonic entropy solutions with a strong contact discontinuity over Lipschitz wall governed by the two-dimensional steady exothermically reacting Euler equations, when the total variation of both initial data and the slope of Lipschitz wall is sufficiently small. Local and global estimates are developed and a modified Glimm-type functional is carefully designed. Next the validation of the quasi-one-dimensional approximation in the domain bounded by the wall and the strong contact discontinuity is rigorous justified by proving that the difference between the average of weak solution and the solution of quasi-one-dimensional system can be bounded by the square of the total variation of both initial data and the slope of Lipschitz wall. The methods and techniques developed here is also helpful for other related problems.

中文翻译：

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Lipschitz 壁上具有强接触不连续性的二维稳定超音速放热反应欧拉流

在本文中，当初始数据和 Lipschitz 壁斜率的总变化足够小时，我们建立了由二维稳定放热反应欧拉方程控制的 Lipschitz 壁上具有强接触不连续性的超音速熵解的全局存在性. 开发了局部和全局估计，并精心设计了修改后的 Glimm 型函数。接下来，通过证明弱解的平均值与拟一维系统的解之间的差异可以有界，严格证明了在由壁和强接触不连续性限定的域中的准一维近似的验证由初始数据和 Lipschitz 壁斜率的总变化的平方。