Journal of the
Korean Mathematical Society JKMS

In this paper we consider a Riemann problem, in particular, the case of the presence of the semi-hyperbolic patches arising from a transonic shock in simple waves interaction. Under this circumstance, we construct global solutions of the two-dimensional Riemann problem of the pressure gradient system. We approach the problem as a Goursat boundary value problem and a mixed initial-boundary value problem, where one of the boundaries is the transonic shock.

Keywords: 2-D Riemann problem, characteristic decomposition, simple waves, transonic shocks

MSC numbers: Primary 35L65, 35J70, 35R35