A singularly perturbed problem for stable supersonic flow (Q1807866)

The author studies the steady-state shock layer solution of a singularly perturbed boundary value problem modeling transonic flow in a nonuniform duct. Lower and upper bounds of the shock location are derived for a special form of the cross-sectional area of the duct. The asymptotic behavior of the solution is given using the method of differential inequalities. Similar and more precise results have already been obtained by \textit{K. Chang} and \textit{F. Howes} [Nonlinear singular perturbation phenomena: theory and applications. Appl. Math. Sci. 56, New York etc.: Springer-Verlang (1984; Zbl 0559.34013)].