  We are concerned with the two-dimensional steady supersonic reacting Euler
flow past Lipschitz bending walls that are small perturbations of a convex one,
and establish the existence of global entropy solutions when the total
variation of both the initial data and the slope of the boundary is
sufficiently small. The flow is governed by an ideal polytropic gas and
undergoes a one-step exothermic chemical reaction under the reaction rate
function that is Lipschtiz and has a positive lower bound. The heat released by
the reaction may cause the total variation of the solution to increase along
the flow direction. We employ the modified wave-front tracking scheme to
construct approximate solutions and develop a Glimm-type functional by
incorporating the approximate strong rarefaction waves and Lipschitz bending
walls to obtain the uniform bound on the total variation of the approximate
solutions. Then we employ this bound to prove the convergence of the
approximate solutions to a global entropy solution that contains a strong
rarefaction wave generated by the Lipschitz bending wall. In addition, the
asymptotic behavior of the entropy solution in the flow direction is also
analyzed.
