Sonic-supersonic solutions for a reactive transonic small disturbance model

This paper is concerned with the structure of supersonic solutions near sonic curves for a transonic small disturbance model derivable from the two-dimensional steady viscous channel flow of a reactive premixed fluid. The model is a second-order nonhomogeneous nonlinear mixed-type equation which is coupled with an ordinary differential equation for the calculation of the reactant mass fraction. We establish the existence of classical sonic-supersonic solutions to its boundary value problem with data given on a smooth sonic curve. To deal with the sonic degeneracy, we first construct a smooth solution in a partial hodograph coordinate system by using the iteration method in a weighted metric space and then express the solution in terms of the original variables. (c) 2021 Elsevier Inc. All rights reserved.