  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.
